Ohio Rev. Code Ann. § 5122.43
(A) Costs, fees, and expenses of all proceedings held under this chapter shall be paid as follows:
(B) A county shall pay for the costs, fees, and expenses described in division (A) of this section with money appropriated pursuant to section 2101.11 of the Revised Code. A county may seek reimbursement from the department of mental health and addiction services by submitting a request and certification by the county auditor of the costs, fees, and expenses to the department within two months of the date the costs, fees, and expenses are incurred by the county. Each fiscal year, based on past allocations, historical utilization, and other factors the department considers appropriate, the department shall allocate for each county an amount for reimbursements under this section. A county's allocation may be zero. The department shall set aside an amount in addition to the allocations to cover court costs associated with proceedings held under this chapter for counties that received an allocation of zero but that incurred expenditures authorized by the department. The total of all the allocations plus the additional amount set aside shall equal the amount appropriated for the fiscal year to the department specifically for the purposes of this section. On receipt, the department shall review each request for reimbursement and prepare a voucher for the amount of the costs, fees, and expenses incurred by the county, provided that the total amount of money paid to all counties in each fiscal year shall not exceed the total amount of moneys specifically appropriated to the department for these purposes. The department's total reimbursement to each county shall be the lesser of the full amount requested or either the amount allocated for the county under this division, or, for counties that received an allocation of zero, the amount approved by the department. In addition, the department shall distribute any surplus remaining from the money appropriated for the fiscal year to the department for the purposes of this section as follows to counties whose full requests exceed their allocations: