Tenn. Code Ann. § 67-8-204

In addition to any inheritance, succession and/or estate tax or taxes imposed by the state of Tennessee under the authority of any other statute or statutes, a Tennessee estate tax is imposed for the exclusive use of the state upon the transfer of the Tennessee estate of every decedent, the amount of which Tennessee estate tax shall be equal to the extent, if any, of the excess of the credit over the aggregate of state taxes, payable by or out of the Tennessee estate of the decedent, or any part thereof; provided, that such Tennessee estate tax imposed shall in no case exceed the extent to which its payment will effect a saving or diminution in the amount of the federal estate tax, payable by or out of the estate of the decedent had this part not been enacted.