Tennessee Code Title 49. Education § 49-2-1101

(a) The boards of education of any two (2) or more school systems are authorized and empowered to establish, maintain and operate a public school or schools jointly by entering into contracts for that purpose.

(b) Upon the execution of contracts under this part by the respective boards of education, the contracts shall be binding upon the boards of education and upon the counties, cities and special school districts involved.

(c) In cities that are authorized by their charters to operate school systems, either the board of education or the city governing body, if the city does not have a board of education, may exercise any authorities or rights granted by parts 5 and 10-13 of this chapter, specifically including contracting with the county for operation, maintenance or improvement of schools within the city.