Ohio Revised Code Title LI. Public Welfare § 5121.53

The state shall bear the expense of the burial or cremation of an indigent patient who dies in a hospital if the body is not claimed for interment or cremation at the expense of friends or relatives, or is not delivered for anatomical purposes or for the study of embalming in accordance with section 1713.34 of the Revised Code. The managing officer of the hospital shall provide at the grave of the patient or, if the patient's cremated remains are buried, at the grave of the patient's cremated remains, a metal, stone, or concrete marker on which shall be inscribed the name and age of the patient and the date of death.