Tenn. Code Ann. § 7-81-402

No ordinance shall become a law without having been passed at two (2) separate meetings by a majority of all the votes of the town and signed by the mayor. It is the duty of the mayor to carefully examine all ordinances passed, and should any of them not meet such mayor's approbation, to return the ordinance to the next meeting of the assembly with such mayor's objection in writing. No law or ordinance so vetoed by the mayor shall go into effect unless the law or ordinance be passed by a majority of the whole number of voters of the town. If the mayor fails to return any ordinance to the next meeting of the assembly, such mayor shall be deemed to have approved the ordinance, and the ordinance shall take effect without further action.