Ohio Revised Code Title LI. Public Welfare § 5122.36

If the legal residence of a person with a mental illness is in another county of the state, the necessary expense of the person's return is a proper charge against the county of legal residence. If an adjudication and order of hospitalization by the probate court of the county of temporary residence are required, the regular probate court fees and expenses incident to the order of hospitalization under this chapter and any other expense incurred on the person's behalf shall be charged to and paid by the county of the person's legal residence upon the approval and certification of the probate judge of the county of the person's legal residence. The ordering court shall send to the probate court of the person's county of legal residence a certified copy of the commitment order from the ordering court. The receiving court shall enter and record the commitment order. The certified commitment order is prima facie evidence of the residence of the person. When the residence of the person cannot be established as represented by the ordering court, the matter of residence shall be referred to the department of mental health and addiction services for investigation and determination.