Ohio Revised Code Title III. Counties § 301.24

The electors of any county may establish, by charter provision, a county department or agency for the administration of public health services. The authorities provided in accordance with the county charter shall exercise all the powers and perform all the duties which are vested in or imposed upon the authorities of city or general health districts. All health districts shall thereupon be abolished within the county, and the county shall succeed to the property, rights, and obligations of such districts. The department of health shall have the same powers with respect to a county health department or agency as it possesses with reference to a general health district. A county health department or agency may participate in any state grants for the expenses of local health administration on the same basis and to the same degree as a general health district.