U.S. District Judge Timothy Black ruled in Cincinnati in December Ohio must recognize same-sex marriages on death certificates if the marriages were performed legally in states where they are permitted.
Ohio voters approved an amendment in 2004 saying same-sex marriages are illegal in Ohio and the state cannot recognize same-sex marriages performed in other states.
The judge said in his ruling a state cannot discriminate against gay couples simply because voters don't like homosexuality, USA Today reported.
Attorney General Mike DeWine's appeal goes to the U.S. Court of Appeals for the Sixth Circuit, headquartered in Cincinnati.
The Ohio dispute is one of a stream of cases involving same-sex marriage in federal court.
The U.S. Supreme Court has stayed, pending appeal, a judge's ruling that struck down Utah's same-sex marriage ban. Earlier in January, a federal judge struck down Oklahoma's ban, but stayed his own ruling pending appeal.