Tenn. Code § 67-8-502
In any case in which this state and one (1) or more other states each claims that it was the domicile of a decedent at the time of death, and no judicial determination of domicile for inheritance tax purposes has been made in any such states, any executor, or the taxing official of any such state, may elect to invoke this part. Such election shall be evidenced by the sending of a notice by registered mail, receipt requested, to the taxing officials of each such state, and to each executor, ancillary administrator and interested person. Any executor may reject such election by sending a notice by registered mail, receipt requested, to the taxing officials involved and to all other executors within forty (40) days after the receipt of such notice of election. If such election be rejected, no further proceedings shall be had under this part. If such election be not rejected, the dispute as to the inheritance taxes shall be determined solely as provided in this part, and no other proceedings to determine or assess such inheritance taxes shall thereafter be instituted in the courts of this state or otherwise.
T.C.A. § 67-8-502