Tennessee Code Title 30. Administration of Estates § 30-1-104

(a)(1) Whenever a nonresident of the state qualifies in this state as the executor or administrator of a person dying in or leaving assets or property in this state, for the purpose of suing or being sued, or for the purpose of being cited or otherwise notified by the court in which the decedent's estate is being administered, the nonresident shall be deemed to have assented to be treated as a resident citizen of this state.

(2) In case it is desired by any citizen or resident of this state to sue the administrator or executor in the administrator's or executor's official capacity for any debt or demand, due or owing to any citizen or resident of this state, from the testator or intestate, then, in case of the inability of the officer in whose hands process is placed to find the administrator or executor in this state, notice of the suit, served upon the clerk of the probate court of the county in which the party qualified as administrator or executor, shall be sufficient notice to bring the administrator or executor before the court issuing the process; provided, that the clerk shall notify by United States registered return-receipt mail the executor or administrator of notice having been served upon the clerk.