The U.S. Supreme Court on Tuesday declined to hear an appeal in the case of a gay couple who sued the Louisiana state registrar after she refused to include both parents' names on their adopted son's updated birth certificate.

Lambda Legal had petitioned the high court to review the case, Adar v. Smith, in which Oren Adar and Mickey Smith sought for both their names to be listed on the birth certificate of the Louisiana-born son they adopted in New York in 2006. The Louisiana state registrar Darlene Smith has refused to recognize the adoption because Adar and Smith, who now live in California, are not legally married.

The suit filed in 2007 claimed that Smith was violating the Full Faith and Credit Clause and Equal Protection Clause of the U.S. Constitution that binds states to the judgments issued by courts in other states. U.S District Judge Jay Zainey ruled for the plaintiffs in 2008, and a three-judge panel of the Fifth Circuit Court of Appeals unanimously affirmed the judgment last year. The full Court of Appeals issued a decision this year overturning the prior decision upon a rehearing at the request of the Louisiana attorney general.

"By denying this writ, the Supreme Court is leaving untouched a dangerous Fifth Circuit Court of Appeals ruling that carves out an exception to the Full Faith and Credit Clause of the U.S. Constitution and to the uniformly recognized respect for judgments that states have come to rely upon," said Kenneth D. Upton, supervising senior staff attorney for Lambda Legal in Dallas, in a statement. "This decision leaves adopted children and their parents vulnerable in their interactions with officials from other states."

"More particularly, this decision leaves a child without an accurate birth certificate listing both his parents," he added. "This issue now moves into the legislative arena. We need to push for a change in Louisiana state policy in order to stabilize and standardize respect for parent-child relationships for all adoptive children."

The high court issued its decision not to review the case without comment.

Family Equality Council, which brought the case to the attention of Lambda Legal, issued a statement expressing disappointment.

"My heart breaks for these parents, and for children across the country who lack the legal relationship with their parents," said executive director Jennifer Chrisler. "A growing number of LGBT parents are creating their families through adoption and although they are bound together by love, we cannot allow states to deny them legal recognition."