Tennessee Code Title 2. Elections § 2-8-111

(1) The county legislative body may cast the deciding vote for offices filled by the votes of a single county or civil district, or, in the alternative, the legislative body may by resolution call for a run-off election between the tied candidates;

(2) The municipal legislative body shall cast the deciding vote for municipal offices, or, in the alternative, the legislative body may by resolution call for a run-off election between the tied candidates;

(3) The governor shall cast the deciding vote for representatives in congress;

(4) The election shall be void if it is for senator in congress, and the governor shall immediately issue an order directing the holding of a special election for the office; and

(5) The general assembly in joint convention shall cast the deciding vote for governor.