Ohio Rev. Code § 3511.10: Voting at board of elections.

A uniformed services or overseas absent voter may cast absent voter's ballots in person at the office of the board of elections in accordance with section 3509.051 of the Revised Code. If thereafter, and before the close of business on the seventh day preceding such election, the board provides additional separate official issue or special election ballots, as provided for in section 3511.04 of the Revised Code, the board shall promptly, and not later than the close of business on the seventh day preceding the day of election, mail such additional ballots to such person at the address specified by that person for that purpose.