Ohio Rev. Code § 5153.39
Immediately upon the organization of the joint board of county commissioners as provided by section 5153.36 of the Revised Code, or as soon thereafter as practicable, such joint board of county commissioners shall appoint a board of five trustees, which shall hold office and perform it duties until the first annual meeting after the choice of an established site and buildings or after the selection and purchase of a building site, at which time such joint board of county commissioners shall appoint a board of five trustees, one of whom shall hold office for the term of one year, one for the term of two years, one for the term of three years, one for the term of four years, and one for the term of five years. Annually thereafter, the joint board of county commissioners shall appoint one trustee, who shall hold his office for the term of five years. The annual meeting of the board of trustees shall be held on the first Tuesday of May in each year.
R.C. §5153.39