Tenn. Code Ann. § 68-2-605

Municipalities located in counties establishing county health departments are empowered to cooperate in the maintenance of county health departments, and to have the county health departments serve as departments for the municipalities, and are authorized to incur the expenses necessary for their proportionate part in the establishment and maintenance of the county health departments, and to levy and collect taxes upon all of the property within the jurisdiction of the municipalities, as may be necessary to meet and pay the expenses.