Ohio Rev. Code § 5153.48
When an established site and buildings are used for a district children's home the joint board of county commissioners organized under section 5153.36 of the Revised Code shall cause the value of such site and buildings to be properly appraised. This appraisal value, or in case of the purchase of a site, the purchase price and the cost of all betterments and additions thereto, shall be paid by the counties comprising the district, in proportion to the taxable property of each county, as shown by its tax duplicate. The current expense of maintaining the home and the cost of ordinary repairs thereto shall be paid by each such county in proportion to the number of children from such county who are maintained in the home during the year.
R.C. §5153.48