The U.S. Supreme Court on Monday ruled in favor of same-sex couples who complained that an Arkansas birth certificate law discriminated against them, reversing a state court's ruling that married lesbian couples must get a court order to have both spouses listed on their children's birth certificates.

Justices issued an unsigned order siding with a Pulaski County judge who struck down part of the state's birth certificate law that defines parents by gender. The state Supreme Court in December reversed that judge's decision, but the U.S. high court said that ruling conflicts with its 2015 Obergefell v. Hodges ruling legalizing gay marriage nationwide.

"The Arkansas Supreme Court's decision, we conclude, denied married same-sex couples access to the 'constellation of benefits that the state has linked to marriage,'" the court said Friday.

Justices Neil Gorsuch, Clarence Thomas and Samuel Alito dissented from the ruling. In the dissenting opinion, Gorsuch wrote that "nothing in Obergefell indicates that a birth registration regime based on biology, one no doubt with many analogues across the country and throughout history, offends the Constitution."

Monday's ruling sent the case back to the state Supreme Court. The state Department of Health said it will take information from same-sex couples who want to amend a birth certificate, but was waiting on guidance from the state's high court. Attorney General Leslie Rutledge, a Republican, said she disagreed with the court's ruling.

"Nonetheless, the Supreme Court has spoken, and I will continue to review today's decision to determine the appropriate next steps upon remand to the Arkansas Supreme Court to ensure that the law is followed properly," she said in a statement. Read more via ABC