Ohio Rev. Code § 3375.10
In any township in which there has been established by a vote of the electors of such township, prior to September 4, 1947, a free public library, such library shall be under the control and management of a board of trustees consisting of three members to be appointed by the board of township trustees. Such members shall be qualified electors of the township. All vacancies on such board of trustees shall be filled by the board of township trustees by appointment. The members of such board of trustees shall serve without compensation. Such board of trustees shall organize in accordance with section 3375.32 of the Revised Code and shall have the control and management of the township free public library. In the exercise of such control and management the board of trustees shall be governed by sections 3375.33 to 3375.41, inclusive, of the Revised Code. This section does not affect the term of any member of a board of library trustees of a township free public library appointed prior to September 4, 1947.
R.C. § 3375.10