Ohio Rev. Code § 503.24
If there is a vacancy by reason of the nonacceptance, death, or removal of a person chosen to an office in any township at the regular election, or if there is a vacancy from any other cause, the board of township trustees shall appoint a person having the qualifications of an elector to fill such vacancy for the unexpired term or until a successor is elected.
If a township is without a board or if no appointment is made within thirty days after the occurrence of a vacancy, a majority of the persons designated as the committee of five on the last-filed nominating petition of the township officer whose vacancy is to be filled who are residents of the township shall appoint a person having the qualifications of an elector to fill the vacancy for the unexpired term or until a successor is elected. If at least three of the committee members who are residents of the township cannot be found, or if that number of such members fails to make an appointment within ten days after the thirty-day period in which the board of township trustees is authorized to make an appointment, then the presiding probate judge of the county shall appoint a suitable person having the qualifications of an elector in the township to fill the vacancy for the unexpired term or until a successor is elected.
If a vacancy occurs in a township elective office more than forty days before the next general election for municipal and township officers a successor shall be chosen at that election to fill the unexpired term, provided the term does not expire within one year from the day of the election. If the term expires within one year from the day of the next general election for municipal and township officers, a successor appointed pursuant to this section shall serve out the unexpired term.
R.C. § 503.24