Tennessee Code Title 29. Remedies and Special Proceedings § 29-20-404

(a) A governmental entity or the insurer of such governmental entity shall not be held liable for any claim arising under state law for which the governmental entity has immunity under this chapter unless the governmental entity has expressly waived such immunity. A governmental entity or the insurer of such governmental entity shall not be held liable for any judgment in excess of the limits of liability set forth in § 29-20-403, unless the governmental entity has expressly waived such limits. The waiver of such immunity or such limits of liability by a governmental entity shall only be valid if such waiver is expressly contained in the provisions or endorsement of a policy or contract of insurance authorized by this chapter to cover its liability under this chapter.

(b) This chapter shall not be construed to prohibit or limit a governmental entity from purchasing a policy or contract of insurance in such amounts of coverage as it deems proper for liabilities which may arise under federal law. If a governmental entity has such policy or contract of insurance for liabilities which may arise under federal law, such policy or contract of insurance shall not be construed or deemed a waiver of any immunity provided in this chapter or of the limits of liability set forth in § 29-20-403, for any claims arising under state law.