Ohio Revised Code Title LI. Public Welfare § 5121.54

If payment of any amount due the state under the provisions of this chapter is made on account of a patient by any liable relative, as defined in section 5121.30 of the Revised Code, the relative may recover from the patient, the patient's guardian, or the executor or administrator of the patient's estate, the full amount of payment made by the liable relative; provided, that in no event may a relative recover in total more than the relative has paid the state, and provided, that in no event is the person from whom recovery is sought obliged to pay at a rate of support higher than the person would have paid had the state proceeded directly against that person.