Ohio Revised Code Title III. Counties § 329.42

The county auditor of the county with the largest population that formed a joint county department of job and family services under section 329.40 of the Revised Code shall serve as the fiscal officer of the joint county department, and the county treasurer of that county shall serve as the treasurer of the joint county department, unless the counties that formed the joint county department agree to appoint the county auditor and county treasurer of another county that formed the department.  In either case, these county officers shall perform any applicable duties for the joint county department as each typically performs for the county of which the individual is an officer.  The board of directors of the joint county department may pay to that county any amount agreed upon by the board of directors and the board of county commissioners of that county to reimburse the county for the costs that are properly allocable to the service of its officers as fiscal officer and treasurer of the joint county department.