( CNN ) -- Mississippi 's lone abortion clinic can stay open , after a federal appeals court Tuesday ruled against a law that effectively would have shut it down -- contending that it 's not right to simply pass the buck to other states . Tuesday 's decision by the 5th U.S . Circuit Court of Appeals spares the Jackson Women 's Health Organization , at least for now . The law 's sponsor , state Rep. Sam Mims , said Tuesday that `` all the parties involved are looking '' at what to do next -- including a possible appeal that could end up before the U.S. Supreme Court . It all stems from House Bill 1390 , legislation signed into law in 2012 that requires abortion doctors to have admitting privileges at a local hospital . Three doctors work in the clinic in the Mississippi capital , only one of whom meets this requirement . Seven hospitals in and around Jackson rebuffed the other two doctors ' requests to get the same privileges -- not because of their qualifications , per se , but because their `` medical practice is inconsistent with '' the hospitals ' practices . State 's clinic faced threat of shutdown . As the appeals court noted Tuesday , this is n't a matter of whether abortion is legal : The Supreme Court `` long ago '' established that it is . `` The ultimate issue in this appeal is whether the state of Mississippi can impose a regulation that effectively will close its only abortion clinic , '' the judges wrote in the prevailing opinion . The state had ceded this fact , contending that Mississippi residents still could get an abortion in Tennessee , Louisiana , Alabama or elsewhere . But that did n't satisfy the appeals court . `` We ... hold that Mississippi may not shift its obligation to respect the established constitutional rights of its citizens to another state , '' the judges wrote . `` Such a proposal would not only place an undue burden on the exercise of a constitutional right , but would also disregard a state 's obligation under the principle of federalism -- applicable to all 50 states . '' In a post on its Facebook page , the Jackson Women 's Health Organization cheered the decision and thanked its supporters . Mims expressed disappointment . `` This legislation has always been about the best possible health care for women who receive an abortion , '' he told CNN . `` I still believe that having physicians obtain privileges in a local hospital makes sense . '' Mims noted that other states have similar requirements . One of them is Texas , which had its own regulation held up -- ironically , by the same federal appeals court that ruled on the Mississippi matter . Appeals court upholds parts of Texas abortion law . That decision found that making some women travel less than 150 miles , because of the regulations within the Texas law , `` is not an undue burden . '' But forcing them to cross state lines -- and allowing some states not to offer abortions while others do -- is a different matter . The judges on Tuesday referred to a 1938 Supreme Court decision involving an African-American being denied admission to the University of Missouri 's law school because of his race . The university system offered him , instead , a tuition stipend to go to a law school in another state . A common tie between that case and what 's happening with regarding to the Mississippi abortion clinic is that `` a state can not lean on its sovereign neighbors to provide protection of its citizens ' federal constitutional rights , '' the judges said . Nancy Northup , head of the Center for Reproductive Rights , applauded Tuesday 's appeals court ruling on Mississippi while acknowledging its future is still uncertain . `` For far too long , women in Mississippi have been teetering on the precipice of a reality similar to the dark days before Roe v. Wade , '' Northup said in a news release . `` This is unacceptable , unconstitutional and contrary to the consensus of the strong majority of Americans who do not wish to see Roe 's constitutional protections overturned . '' Mims thinks that House Bill 1390 should still stand , contending that it includes a sensible measure to safeguard women 's health . `` I think it 's a very important piece of legislation that passed the Mississippi Legislature , '' the Republican from McComb said . `` And we 'll have to see what happens next . '' Opinion : Mississippi 's end run around abortion . CNN 's Rich Phillips contributed to this report .
NEW : Rep. Mims disappointed ; he says his bill seeks to give women best possible care . WASHINGTON (CNN) -- Mississippi 's lone abortion clinic cheers the ruling ; supporters say fight is n't over . State law : All clinic doctors had to get privileges at local hospitals ; they could not . The state argued that those wanting abortions could go to nearby states .