Ohio Rev. Code § 3513.18: Primary election pollbooks.

Party primaries shall be held at the same place and time, but there shall be separate pollbooks and tally sheets provided at each polling place for each party participating in the election.

If a special election on a question or issue is held on the day of a primary election, there shall be provided in the pollbooks pages on which shall be recorded the names of all electors voting on said question or issue and not voting in such primary. It shall not be necessary for electors desiring to vote only on the question or issue to declare their political affiliation.