Tenn. Code Ann. § 71-5-2311: Payment for hospitalization

(a) Whenever any hospital has entered into either or both of such contracts with any county, the hospital shall render monthly statements to the county mayor of the county showing the name and address of each patient so received and treated at the expense of the county, and the length of time treated, and an account for the keep of the patient, and whether the patient was treated under the annual contract plan or by special contract with the county mayor as provided in this part.

(b) Upon the presentation of the account, the county mayor shall inspect the account, and if found correct, shall issue a county warrant for same, which shall be paid as other county expenses.