Ohio Revised Code Title XXXV. Elections § 3503.111

The board of elections of any county shall register or change the registration of any person determined not to be a resident in that county under section 3503.02 of the Revised Code, who is a resident and a qualified elector of another county in this state, on behalf of the county of residence.

The director of any board of elections registering a person under this section shall send the completed registration form of that person to the director of the board of elections of the county of residence, who shall enter the form in the proper registration files and shall promptly send an acknowledgment notice as prescribed by the secretary of state to the registrant at the new address listed on the registration form.