The US Supreme Court has refused to hear the case of a gay couple who wanted both their names on the birth certificate of a boy they adopted.

Oren Adar and Mickey Smith, of New Orleans, adopted the Louisiana-born boy in 2006 in New York.

The unmarried couple requested a birth certificate but Louisiana’s registrar, Darlene Smith, said she could not put both their names on the birth certificate because Louisiana only allows married couples to adopt.

Mr Adar and Mr Smith filed a lawsuit with gay rights group Lambda Legal in October 2007 and argued that the registrar’s decision violated the US constitution an should have recognised the New York adoption judgment.

Although lower courts sided with the couple, the Fifth Circuit Court of Appeals against them in a rehearing.

Kenneth D Upton, a supervising senior staff attorney at Lambda Legal, said: “This decision leaves adopted children and their parents vulnerable in their interactions with officials from other states.”

He added: “Unfortunately, same–sex parents who have or plan to adopt children are treated differently from state to state at this point. So we urge parents to check with an attorney and take every step they can to protect their families – and to call Lambda Legal’s HelpDesk if they need more information.”