Ohio Rev. Code § 3707.17
When a person with a contagious disease, quarantined in a county by a city or general health district, has a legal settlement in a municipal corporation or township within the same county but other than that in which quarantined, or has a legal settlement in another county of the state, and such person is unable to pay the expenses of the service provided under section 3707.14 of the Revised Code, the city or general health district rendering such service shall notify in writing the proper officials of the municipal corporation or township of legal settlement or the board of county commissioners of the county of legal settlement if such legal settlement is in another county that such services are being rendered. Such notice shall be sent within three days if the fact of nonresidence is disclosed upon the beginning of such service or admission to a hospital or other institution of quarantine, or within three days after the discovery of such fact if it is not so disclosed. Within twenty days after the discharge of such quarantined person, the health commissioner of the city or general health district shall send a notice of such discharge and a sworn statement of the expenses, either actual or at the established rate of the hospital or other institution of quarantine, to the proper officials of the municipal corporation or township of legal settlement or the board of county commissioners of the county of legal settlement if such legal settlement is in another county. Thereupon the municipal corporation or township of legal settlement or county of legal settlement if such legal settlement is in another county shall be liable to the city or general health district rendering such service, and shall pay for it within thirty days after date of the sworn statement of expenses. If the notice of the rendering of such service, required to be sent by the health commissioner, is not sent within three days after the disclosure by the person quarantined or the discovery of such nonresidence, the municipal corporation or township of legal settlement or the county of legal settlement if such legal settlement is in another county shall be liable only after the receipt of such notice.
This section does not prevent the removal of such quarantined person by the municipal corporation, township, or county of legal settlement, at its expense, but such removal shall not relieve the municipal corporation, township, or county of legal settlement for the expenses previously incurred by the city or general health district in which such person has been quarantined. Any such person who does not, upon discharge, pay the expenses of such quarantine shall be deemed indigent insofar as the city or general health district is concerned. The municipal corporation, township, or county of legal settlement is hereby subrogated to all the rights of the city or general health district in which such service was rendered.
R.C. §3707.17