Ohio Rev. Code § 124.54
Where a municipal civil service commission serves a city school district whose territory is located in more than one city, the board of education of such district shall, by resolution, appropriate each year, to be paid into the treasury of the municipal civil service commission's city, an amount sufficient to meet the portion of the board of education's cost of civil service administration. The amount shall be mutually agreed to by the school board and the commission or if agreement cannot be reached, it shall be determined by the ratio of the number of employees of such board in the classified service to the entire number of employees in the classified service in all political divisions served by the commission.
Where a municipal civil service commission serves a city school district whose territory is not located in more than one city, the board of education of such district may appropriate such an amount to be paid to the city's treasury.
R.C. §124.54