Can a tub and shower share the same drain?
Of course they can as long as you have proper drainage angle and double venting and traps.  If this is an installation of a new fixture, you need a permit and a master plumber to sign for the permit.  Get a plumber and do it right. Just asking the question tells me you don't know what to do and could get into trouble.  Saving a few bucks and doing it wrong will cost you so much more in the short and long run. Some things have to be left to the licensed professionals.