Lawyers for both the state and a group of gay and lesbian couples hoping to topple Louisiana’s ban on same-sex marriage submitted arguments late Wednesday on two separate questions: whether the ban violates the First Amendment or the due process clause of the U.S. Constitution.

Attorneys in the case have already made oral arguments before U.S. District Judge Martin Feldman in federal court, but debated only whether Louisiana must recognize same-sex marriages performed legally in other states.

New legal briefs requested by the judge after that hearing address the question of whether Louisiana must actually hand out marriage licenses to same-sex couples, and whether the state is violating First Amendment rights against so-called compelled speech by requiring that same-sex couples who have already wed elsewhere list themselves as single on tax returns.

The couples involved answered both questions in the affirmative. They made their case that Louisiana is forcing those married couples into “evident hypocrisy” by requiring same-sex couples, even if they have a legal marriage license from another state, to list themselves as single on Louisiana tax forms, violating the First Amendment in the process.

They also argued that denying same-sex couples a marriage license in Louisiana bas

The first argument may be a unique one, though similar gay marriages cases are pending in every state. The second relies on the same line of reasoning employed in dozens of those lawsuits, most of them sparked by the U.S. Supreme Court’s decision last year in United States v. Windsor, holding that the federal government must extend benefits to same-sex couples married in states where those unions are legal.

The plaintiffs’ brief on Wednesday quotes Justice Anthony Kennedy, who in voting to strike down part of the federal Defense of Marriage Act in the Windsor case argued that singling out same-sex couples “demeans” them and “humiliates” the children already being raised by them.

Lawyers for Attorney General Buddy Caldwell and the other named defendants in the case responded unequivocally. The answer to whether Louisiana is violating either the First Amendment or due process rights of same-sex couples, they wrote, “is ‘no.’”

As they did in court last month, they pointed out that the Supreme Court in Windsor affirmed the right of the states — rather than judges or the federal government — to define marriage. Kennedy wrote that the states have a “historic and essential authority to define the marital relation.”

The state’s brief acknowledges that the couples involved have hit upon a “novel” argument by bringing up the First Amendment, but then dismiss it as off base.

“This novel claim has no merit because this tax filing requirement regulates conduct, not speech,” it reads, “And therefore does not implicate the First Amendment compelled-speech doctrine at all.”