Tennessee Code Title 41. Correctional Institutions and Inmates § 41-4-139

(a) Whenever the chief executive officer of any county penal farm certifies on or before the tenth day of each month to the judicial cost accountant the state prisoners kept in the institution and the number of days each was kept in the institution during the preceding month, the judicial cost accountant shall cause to be paid to the county the subsidy for that county as fixed by provisions of chapter 8 of this title and the contracts entered into pursuant thereto.

(b) For the purposes of this section, “county penal farm” is construed to include city jails in those municipalities that have concurrent jurisdiction with general sessions courts over state misdemeanors. The municipality shall be compensated in the same manner and conditions as counties are compensated.