Ohio Rev. Code § 9.15
As used in this section, "legal residence" means a permanent place of abode used or occupied as living quarters at the time of a person's death, including a nursing home, hospital, or other care facility.
When the body of a dead person is found in a township or municipal corporation, and such person was not an inmate of a correctional, benevolent, or charitable institution of this state, and the body is not claimed by any person for private interment or cremation at the person's own expense, or delivered for the purpose of medical or surgical study or dissection in accordance with section 1713.34 of the Revised Code, it shall be disposed of as follows:
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.
R.C. § 9.15