The issue of gay marriage in New York is returning to court today, with a panel of appellate judges in Brooklyn scheduled to hear arguments on whether the state must recognize same-sex marriages performed elsewhere.

New York State currently does not permit gay couples to marry but has, for the most part, recognized unions that have been performed out of state. Just last month, Governor Paterson took steps to ensure that all state agencies recognized gay marriages performed elsewhere.

But whether the Legislature or the courts will allow Mr. Paterson to set the policy on this issue remains to be seen.

The case being heard today, Godfrey v. Spano, will consider whether recognition of same-sex marriages first requires approval from the Legislature. So far the Legislature hasn’t passed any laws relating to gay marriage.

Whatever decision the Brooklyn appeals court reaches in the Godfrey case is sure to be quickly appealed to the state’s highest court, the Court of Appeals.

The lawsuit, which is being litigated by a Christian legal group based in Arizona, predates Mr. Paterson’s pronouncement. It is a challenge to a similar marriage recognition policy by the Westchester county executive, Andrew Spano. The suit, filed in 2006, is brought in the name of four Westchester county residents who say the policy brings “injury and mischief” to local taxpayers because it will extend spousal benefits to the spouses of gay county employees who entered into same-sex marriages out of state.

Massachusetts and California are the only two states that perform gay marriages. Canada also conducts such marriages.

New York State has long recognized out-of-state marriages between men and women who are not eligible for marriage in this state. In one oft-cited precedent, the state recognized a Rhode Island marriage of an uncle and niece. The main legal question before the court is whether that principle applies to same-sex unions.

The case may well turn on how the court defines marriage.

A lawyer for the Arizona group, the Alliance Defense Fund, argues in an appellate brief that this marriage recognition rule “does not apply to same-sex unions, regardless of whether they are labeled a ‘marriage,’ because a same-sex union, by definition, does not qualify as a marriage.” In support, the group’s lawyer, Brian Raum, quotes from several dictionary definitions of the word “marriage,” including one popular in the 1700s.

A gay rights organization, Lambda Legal, which represents a gay married couple from Westchester in the case, argues that the marriage-recognition principle must extend to gay marriages.

“This action should be recognized for what it is — a bald maneuver to impair the rights of lesbian and gay New Yorkers by ideologically motivated plaintiffs and counsel who cannot countenance that government officials are applying New York law evenhandedly to these residents,” a Lambda Legal lawyer, Susan Sommer, argued in an appellate brief.

The Alliance Defense Fund recently filed a similar suit challenging Mr. Paterson’s marriage-recognition policy. The group dates back to 1994 and was founded by prominent evangelical Christians, including the evangelists William Bright, D. James Kennedy, and the president of Focus on the Family, James Dobson.