Ohio Revised Code General Provisions § 9.15

(A) If the person was a legal resident of the county, the proper officers of the township or municipal corporation in which the person's body was found shall cause it to be buried or cremated at the expense of the township or municipal corporation in which the person had a legal residence at the time of death.

(B) If the person had a legal residence in any other county of the state at the time of death, the superintendent of the county home of the county in which such body was found shall cause it to be buried or cremated at the expense of the township or municipal corporation in which the person had a legal residence at the time of death.

(C) If the person was an inmate of a correctional institution of the county or a patient or resident of a benevolent institution of the county, the person had no legal residence in the state, or the person's legal residence is unknown, the superintendent shall cause the person to be buried or cremated at the expense of the county.

Such officials shall provide, at the grave of the person or, if the person's cremated remains are buried, at the grave of the person's cremated remains, a metal, stone, or concrete marker on which the person's name and age, if known, and date of death shall be inscribed.

A political subdivision is not relieved of its duty to bury or cremate a person at its expense under this section when the body is claimed by an indigent person. As used in this section, “indigent person” means a person whose income does not exceed one hundred fifty per cent of the federal poverty line, as revised annually by the United States department of health and human services in accordance with section 673(2) of the “Omnibus Budget Reconciliation Act of 1981,” 95 Stat. 511, 42 U.S.C. 9902, as amended, for a family size equal to the size of the person's family.