Ohio has partisan primaries for judicial offices, but in the general election there is no party label for judicial nominees. On April 21, the Ohio Senate passed SB 80. It says there should be partisan labels on general election ballots, starting in 2022, for State Supreme and State Appellate races. It passed the Senate on a party-line vote, with Republicans in favor and Democrats opposed.
Ironically, some years ago the Ohio Democratic Party filed a federal lawsuit to require party labels on the general election ballot. They lost that lawsuit, and now appear to have changed their mind.