Tennessee Code Title 10. Public Libraries, Archives and Records § 10-3-102

(a) Upon the decision of such county legislative body and/or city governing body to establish, maintain or support a free public library, or to contract with another library for library service, or to contract with one (1) or more counties or cities for joint operation of a free public library, it shall levy for the purpose a property tax, or shall use therefor funds raised by taxes for county or municipal purposes, such a library service being declared to be a county or municipal service.

(b) If a portion of a county is already taxed for maintenance of a free public library, the county legislative body is empowered to levy a tax for a free library on all the property in the county, or the county legislative body may levy a tax on only the property of such portion of the county as is not already taxed for maintenance of a free public library. If a general county-wide tax levy is made for this purpose, the county trustee shall keep the funds raised thereby separate and apart from all other tax funds coming into such county trustee's hands, and shall make quarterly distribution of the same between the county library board and the governing body of the free public library of the city or cities within the limits of the county on the basis of the population enumerated by the most recent federal census. Subject to the preceding sentence, funds raised under §§ 10-3-101 -- 10-3-108 may be contributed toward the maintenance of any free public library maintained by a municipality in such county as provided in § 10-3-101.