WASHINGTON — The Supreme Court on Monday reaffirmed its 2015 decision recognizing a constitutional right to same-sex marriage, ruling that states may not treat married same-sex couples differently from others in issuing birth certificates.

The decision was unsigned. Justice Neil M. Gorsuch, joined by Justices Clarence Thomas and Samuel A. Alito Jr., dissented.

The case concerns an Arkansas law about birth certificates that treats married opposite-sex couples differently from same-sex ones. A husband of a married woman is automatically listed as the father even if he is not the genetic parent. Same-sex spouses are not.

The case, Pavan v. Smith, No. 16-992, was brought by two married lesbian couples who had jointly planned their child’s conception by means of an anonymous sperm donor. State officials listed the biological mother on the children’s birth certificates and refused to list their partners, saying they were not entitled to a husband’s presumption of paternity.