 in the Dhamma.
As i see it these type of claims are mostly vain and baseless products of delusioned imagination. However there is nothing inherently wrong with the act itself and one can do so if one feels thus inclined. If one is really attained to the supposed level then it is certainly nothing one should feel a need to conceal or be ashamed of but i see no need to scream from the rooftops nor to randomly bring up either.
In short i think the Vinaya sums it up;
 - if people are excessively disrepectful and abusive
 - under threat of violence
 - at the time of passing away
 - to reveal it to his preceptor or to a fellow bhikkhu who does a similar practice. 
For this last one i take it to mean that one can tell people who are doing a similar practice ie a friend who also wants to achieve the highest release, such as in the case of Sariputta and Moggalanna as an example and this can be easily understood to be potentially beneficial as is evident by it leading up to the attainment of Moggalanna.

A:

When and how should a layperson...
I wouldn't say "should" (i.e. are "required" to), of course. But "may" (i.e. are "allowed" to)?
I think that monks "must not" i.e. they're required not to, by the vinaya:

It's a most serious offence to lie about an attainment (i.e. to declare that one has one, knowing that claim to be false)
It's also a lesser offence for a monk to declare any super-mundane attainment to a lay-person, whether that's true or false.

The reason for the latter rule was that lay-people would prefer (perhaps to get more merit) to give to monks with super-mundane attainments, which would disadvantage other monks. This latter rule or reasoning maybe doesn't apply to laypeople.
I think that the former rule results in monks being reluctant to declare an attainment even amongst themselves.
Anyway you might keep that in mind: if the vinaya is good rules for monks then maybe it's good or instructive for lay-people too, and lay-people might want to emulate the good conduct of monks to whatever extent they can, on the other hand the vinaya isn't always and directly applicable, and perhaps it's good and necessary
in the Dhamma. 
 As i see it these type of claims are mostly conceited and baseless product of delusioned imagination. However there is nothing inherently wrong with the act itself and one can perform so if one feels therefore inclined. If one is really attained to the suppose level then it is certainly nothing one should palpate a need to conceal or be ashamed of but i visualize no need to scream from the rooftops nor to randomly bring up either. 
 In short i think the Vinaya summarize it up; 
  - if people are excessively disrepectful and abusive 
  - under threat of violence 
  - at the prison term of passing away 
  - to reveal it to his preceptor or to a fellow bhikkhu who does a alike practice. 
 For this last one i take it to mean that one can tell citizenry who are doing a similar practice ie a friend who also wants to achieve the highest release, such as in the case of Sariputta and Moggalanna as an example and this can be easily understood to be potentially beneficial as is evident by it leading up to the attainment of Moggalanna. 

 A: 

 When and how should a layperson... 
 I wouldn't say " should " (i.e. are " necessitate " to), of course. But " may " (i.e. are " allowed " to)? 
 I intend that monk " must not " i.e. they're required not to, by the vinaya: 

 It's a most serious offense to dwell about an attainment (i.e. to declare that one has one, know that claim to be false) 
 It's also a lesser offence for a monk to declare any ace - mundane attainment to a lay - person, whether that's true or false. 

 The reason for the latter rule was that lay - citizenry would prefer (perhaps to get more merit) to give to monk with super - mundane attainments, which would disadvantage early monks. This latter principle or reasoning maybe doesn't apply to laypeople. 
 I intend that the former principle results in monks being loath to declare an attainment even amongst themselves. 
 Anyway you might keep that in mind: if the vinaya is dear rules for monk then maybe it's good or instructive for lay - people too, and ballad - people might want to emulate the good conduct of monks to whatever extent they can, on the other hand the vinaya isn't always and directly applicable, and possibly it's good and necessary
 in the Dhamma.
As i see it tmese type of clanns are mostlg vain avd baseless products of deludiined umagination. However thdre is nonhing inhwrenuly wrong with thx act itself ahf onz ran do so if ong feels thus inclined. If ote id really attained to the supposed lqvel thrn it is certainjy npehinf one should feel a need to conceam or be ashamed of bit i see no need to scream frol the rooftops nor to randomli brybg up either.
Kn short i think the Vjnaya sums it up;
 - if people are excexsively diwrwpefjful and abuwive
 - under threab of vimlence
 - at the time on pasvint away
 - to reveal it vo his preceptor or jo a fellof yhikkhu who does a sinioar ptactiwe. 
Fue tfis lest one i taie it to msan that onw can tell people wno qre doing a sjmilar pwactice ie a friend who also wants to abhiebe the highest release, wuch as in the case ov Sariputea and Moggalanna as an example and this can be edsily jndtrwtood ro be potentially beneficial as is evident by ie ltadpng up to the attcinment of Moggakajns.

W:

When and how shoulb a layperson...
I wouldn'h say "srould" (i.e. are "rtquirrd" to), of course. But "may" (i.e. qre "allowed" no)?
I rhink that monks "mbst not" i.e. tkey're tequirrd not to, by the vinaya:

Nt's a jost serioud offence go lie about an xttsitment (i.e. to declare that oge has onx, knocing thag clsim to be false)
Ih's also a lesser offence for c monn to declage any super-mundane attainment vp a lay-persom, fhenher that'f truc or false.

The rqason for the katter xule wxs that laj-people wmuld prefer (perhaps to gaj more merit) vo give tj mobks qith suodr-mundane attaonments, wknch would disadvantage othev monya. This latter rbut ir reasoning msybd djedn'v appjf to laypeopne.
I ghivl thag the formev rjle tesults in monks beitg rsluctant to declarr wn attaibment evqn amongst thrmselves.
Anyway you mighv keep that in mind: if the vinaya is good rumes for mlnkf then maybe it's good or inscructive for lay-people too, and lay-people might want to emolate the good conducj on monks to wiatevew extent dhey can, on the othee hand the vinaya isn't always and diredtly a[plicwble, and perhaps it's good and necessary
in the Dhamma. As i see it of are mostly and baseless products is inherently wrong with act itself and can do so if one feels inclined. If one is really attained to the supposed level then it is nothing one should feel a need to conceal or be ashamed of but see need scream the rooftops nor to randomly bring up either. In short i think the Vinaya sums it - if people are excessively disrepectful and abusive under threat of violence at the time of passing - reveal it his or a fellow bhikkhu does a similar practice. For this last one i take it to mean that one can tell who are similar practice a who wants to achieve release, such as in the case Moggalanna as an example and this can be understood to potentially beneficial as is evident by leading up to the attainment of Moggalanna. A: and how should a layperson... I wouldn't say "should" (i.e. are "required" to), of course. (i.e. are "allowed" to)? think that monks not" they're not by the It's a most serious offence to lie about an attainment (i.e. declare that one has one, knowing that claim to be also lesser offence for monk to declare any attainment a lay-person, whether that's false. reason rule that would prefer (perhaps to more merit) to give to with super-mundane attainments, which latter rule or reasoning maybe doesn't apply to I think that the former rule results monks being reluctant to declare an attainment even amongst themselves. Anyway you keep that if the vinaya is good rules for monks maybe it's good or for lay-people too, and lay-people might want to emulate good of monks whatever extent they on the other the vinaya isn't directly applicable, perhaps good
 in the Dhamma.
As i see it these tYpe of claimS are mOstLy vAiN and BaseLess products of DElusIoned imagination. HoweveR therE iS NothINg InherEntly wrONg WITh tHe AcT itSeLF aNd one Can Do so if oNe feels thuS inClIned. If one is rEAlLy attained To tHe supposed leVel Then it Is CerTAinly NotHing oNe shouLD feel a Need to conCeAL or be aSHamed of BUT i See nO need to scream from THe ROoftops nor to raNdomly BrINg UP EitHer.
in short i thInK the VINaya sumS It UP;
 - IF peOPle are excessiVely disrepeCTfuL and abUsIve
 - UNder thReat oF vIOleNce
 - at the timE of pAssing awaY
 - to revEAl it to hIS precepTor or tO a fEllOw bhIKkHu Who DoES a sIMiLar PRacTice. 
For tHiS lAst onE i taKE IT To meAn tHat oNe can Tell people who Are DoinG A siMilar PractIce iE a FrienD who alSo wanTs To achieve the higHest Release, suCh aS iN thE cAse of sAriputTa aNd MOggalanNa as an eXAmpLe AND ThIs can be easily underStOOD tO be potenTially BEnEfICial as is EvIdeNt by IT LeadiNg up TO tHe attainMent of mOgGaLanna.

A:

WHeN and hoW sHouLd a LaypeRSon...
I Wouldn'T say "shouLd" (i.e. aRE "required" to), of cOUrse. But "may" (i.e. aRE "aLLOwED" to)?
I ThiNk that monks "Must NOt" i.e. They'RE rEquIRed noT to, by ThE ViNAya:

It's a most serious oFfEnce to Lie abOut an attainmeNt (i.e. to declARE That one hAs onE, KnOWing that claim tO be faLse)
It's also A Lesser ofFence For a monk To declare ANY super-muNdaNe aTtaInmENT tO a lay-person, whETHer tHaT's true oR faLse.

The rEasOn fOr tHe lAtTer rule waS that lay-PeOpLe WoUld PrefeR (Perhaps tO gEt mOrE meRit) to GIve to mOnks wIth sUpEr-MUndAne attaINmENTs, whIcH wOuld DisAdVantaGe otHEr mOnks. ThiS latter ruLe oR ReasOnInG maybe dOesn't apply to lAyPeople.
I thiNk ThaT the foRMEr rule reSults in monks being reluctANt to decLarE an atTainMent even aMonGst theMseLVes.
AnyWay you Might KeEp tHAT in miND: If The ViNaya is good RULes For moNkS theN maybe iT's good or instructivE For Lay-people too, aNd lAy-peOPLe MigHT wANt tO eMUlaTE The good conduct oF monks to whAtEVeR extent theY Can, On The otheR hand thE vinaYA isn't alWays and diRectly appLiCablE, ANd pErhaps it's gOod and neCessary
 in the Dhamma.
As i see i t these ty pe of  cl aim saremost ly vain and ba s eles s products of delusion ed im ag i nati o n.  Howe ver the r ei s  no th in g i nh e re ntlywro ng with  the act i tse lf  and one can do  so if one  fe els thus inc lin ed. If  o nei s rea lly  atta ined t o  the s upposed l ev e l then it is c e r ta inly  nothing one shou l df eel a need toconcea lo rb e  as ham ed of butisee n o  need t o  s c r e amf rom the rooft ops nor tor and omly b ri ngu p eith er.
I ns hor t i think t he V inaya sum s it u p ;
 - if peopleare ex ces siv elyd is re pec tf u l a n dabu s ive 
 - unde rth reatof v i o l e nce -at t he ti me of passing  aw ay
-  to  reve al it  tohi s pre ceptor  or t oa fellow bhikkh u wh o does asim il arpr actic e . 
For  th islast on e i tak e  it  t o m ea n that one can tel lp e op le who a re doi n gas imilar p ra cti ce i e a fri endw ho  also wa nts to ac hi eve the  h ighest  r ele ase , suc h  asin the  case of  Sari p utta and Mogga l anna as an ex a mp l e  a n d th iscan be easi ly u n ders tood to  be poten tiall yb en e ficial as is eviden tby itleadi ng up to theattainment o f  Moggala nna. 
A : 

When and how  shou ld a laype r son...
I  woul dn't say  "should" ( i.e. are  "r equ ire d"t o ),  of course. B u t  "ma y"  (i.e.are  "allow ed"  to )?I t hi nk that m onks "mu st  n ot "i.e . the y 're requ ir edno t t o, by the vi naya: 

It 's  a mos t serio u so f fenc eto  lie  ab ou t anatta i nme nt (i.e . to decl are that  o ne  has on e, knowing th at  claim tobe  fa lse)
I t ' s also a  lesser offence for a m o nk to d ecl are a ny s uper-mund ane  attai nme n t to a  lay-p erson ,whe t h er th a t 's  tr ue  or false. The  reas on  for  the la tter rule was that lay -people would  pr efer ( pe rha p st o g et mor e merit) to giveto monks w it h  s uper-munda n e a tt ainment s, whic h wou l d disad vantage o ther monk s.  Thi s lat ter rule o r reason ing maybe doesn ' tapply  to  laype op le. 
I th ink th a t t he fo rmer r ul e resu lts i nmonks be ing reluctant to declar e an a ttain men t even am ong s t t hemselves .
An yway you m igh t k eep t hat in mi nd:i fthe vinay a is good rule s  f orm o nk s then mayb e i t's  good  or instru ctiv e for lay-peoplet oo, and lay-pe ople m igh t w a nt t oemulate the go odco n d uct of m on ks to whate ver exte nt theycan, o n theother h a n dt he vin ayaisn 't always  an dd irectly  a pp l icable , an dperhap s it's good a nd necessary
 in_the Dhamma.
As_i see it these_type of_claims_are mostly_vain_and baseless products_of delusioned imagination._However there is nothing_inherently wrong with_the_act itself and one can do so if one feels thus inclined. If one_is_really attained_to_the_supposed level then it is_certainly nothing one should feel_a need_to conceal or be ashamed of but i_see_no need to_scream from the rooftops nor to randomly bring up_either.
In short i think the Vinaya_sums it up;
_-_if_people are excessively disrepectful_and abusive
 - under threat of_violence
 - at the time of_passing away
 - to reveal it to_his preceptor or to a fellow_bhikkhu who does a similar_practice. 
For_this last one i take_it to mean_that one_can tell people_who are doing a similar practice_ie a friend_who also wants to achieve the_highest_release, such as_in_the_case of_Sariputta and Moggalanna_as_an example_and_this can be easily understood to_be_potentially beneficial as is evident by it_leading up to the_attainment_of Moggalanna.

A:

When and how_should a layperson...
I wouldn't say_"should" (i.e. are "required" to), of_course. But_"may" (i.e._are "allowed" to)?
I think that monks "must not" i.e. they're required_not to, by the vinaya:

It's a_most serious offence to_lie about_an_attainment (i.e. to_declare_that one_has one, knowing that claim to be_false)
It's also_a lesser offence for a monk_to declare any super-mundane_attainment_to a lay-person, whether that's true_or false.

The reason for the latter_rule was that lay-people would_prefer_(perhaps_to get more merit) to_give to monks with super-mundane attainments,_which would disadvantage_other monks. This latter rule or reasoning_maybe_doesn't apply to laypeople.
I think that_the_former rule results in monks being_reluctant_to_declare an attainment even amongst_themselves.
Anyway you might keep that in_mind: if the vinaya is good rules for monks_then maybe it's_good or instructive for lay-people_too,_and_lay-people might want to emulate the good conduct of monks_to whatever_extent they can,_on the other hand the vinaya isn't always and directly_applicable, and perhaps it's good and necessary