The Supreme Court of Arkansas ruled on Thursday that the state can constitutionally refuse to grant lesbian couples a birth certificate that lists their child’s two mothers.

Arkansas state laws laying out how the Department of Health should handle birth certificates allow for the identification only of a “mother” and a “father.” The court said those laws were not in conflict with Obergefell v. Hodges, last year’s landmark Supreme Court ruling that legalized gay marriage nationwide.

“Obergefell did not address Arkansas’s statutory framework regarding birth certificates, either expressly or impliedly,” wrote Justice Josephine Hart, pointing out that the 2015 decision dealt specifically with the right to gay marriage and addressed birth certificates only in passing.

Under the Arkansas statutes, the three married couples who sued the Health Department were issued birth certificates that named only their child’s birth mother. The couples argued this violated their constitutional rights to due process and equal protection of the laws.

All three couples were married and had conceived through artificial insemination from anonymous sperm donors.

Last year, a lower court judge agreed and struck down the laws, leading to a temporary victory for the couples as the Arkansas attorney general and the Health Department decided how to proceed. But days later, the Arkansas Supreme Court put the judge’s order on hold, effectively halting the issuance of birth certificates to same-sex couples in the state.

In its Thursday ruling, the state’s top court reasoned in part that the two main laws at issue don’t implicate gay marriage or the parental rights of same-sex couples, but merely attempt to “truthfully record the nexus of the biological mother and the biological father to the child.”

“On the record presented,” the court’s majority opinion said, “we cannot say that naming the nonbiological spouse on the birth certificate of the child is an interest of the person so fundamental that the State must accord the interest its respect under either statute.”

We cannot say that naming the nonbiological spouse on the birth certificate of the child is an interest of the person so fundamental that the State must accord the interest its respect. Arkansas Supreme Court

This conclusion drew a rebuke from Chief Justice Howard Brill, who disagreed with the decision’s broad constitutional point (although he signed on to a more technical portion of the ruling). He kicked off his opinion with lyrics from the 1964 Bob Dylan classic “The Times They Are a-Changin’.”

“Regardless of personal values and regardless of a belief that the United States Supreme Court may have wrongfully decided a legal issue, all are bound by the law of the land,” Brill wrote.

He and another justice suggested that the Arkansas state legislature should make changes to civil records laws to conform to the new legal landscape, avoid further confusion and prevent needless litigation.

Only one justice, Paul Danielson, was opposed to the entire ruling. He would have treated birth certificates as a marriage benefit that must flow equally to everyone.

“Obergefell requires that this benefit be accorded to same-sex spouses and opposite-sex spouses with equal force,” Danielson wrote.

If the same-sex couples appeal the decision in Smith v. Pavan, the next step would be the U.S. Supreme Court.