Ohio Rev. Code § 3709.31
The treasurer of a city which constitutes a city health district shall be the custodian of the health fund of such city health district. The county treasurer of a county which constitutes all or the major portion of a general health district shall be the custodian of the health fund of the general health district.
The county auditor of a county which constitutes all or a major portion of a general health district shall act as the auditor of the general health district. The auditor of a city which constitutes a city health district shall act as the auditor of a city health district.
Expenses of the board of health of a general health district shall be paid on the warrant of the county auditor issued on vouchers approved by the board of health and signed by the health commissioner or the commissioner's designee. Expenses of a board of health or health department of a city health district shall be paid on the warrant of the auditor of the city issued on vouchers approved by the board of health or health department of a city health district and signed by the health commissioner or the commissioner's designee. A designee of a health commissioner of a general or city health district may sign vouchers only if he has given bond to the board of health in the amount of one million dollars with a company authorized to conduct a surety business in this state as a surety to be held by the board and conditioned on the faithful performance of his duties. The expense or premium of the bond shall be paid by the board and charged to the health fund.
R.C. §3709.31