An amendment to Ohio's constitution passed by voters in 2004 bans same-sex marriage. And the state doesn't recognize same-sex unions formed in other states.
But two men who married same-sex partners elsewhere asked in their suit to be named on their spouses' Ohio death certificates.
Judge Timothy Black ruled that denying the plaintiffs this because they were in same-sex marriages would violate their right to equal protection under the law.
Constitutional law professor Jonathan Entin at Case Western Reserve University says though this was a narrow ruling, it could have broader ramifications if used in future lawsuits.
"There is language in Judge Black's opinion that a plaintiff might use down the road to challenge other policies in Ohio that would deny recognition of out-of-state same-sex marriages involving people who now live in Ohio," Entin said.
But Entin says it's probably less likely this ruling would be used directly to chip away at Ohio's ban on same-sex partners marrying in the state.
In the ruling, Judge Black acknowledges the arguments and evidence presented could be used in broader challenges of Ohio law.
Ohio Attorney General Mike DeWine plans to appeal the decision.