Tennessee Code Title 40. Criminal Procedure § 40-17-209

(a) If a person comes into this state in obedience to a summons directing the witness to attend and testify in this state, the witness shall not, while in this state pursuant to the summons, be subject to arrest or the service of process, civil or criminal, in connection with matters which arose before the witness's entrance into this state under the summons.

(b) If a person passes through this state while going to another state in obedience to a summons to attend and testify in that state, or while returning from that other state, the witness shall not, while so passing through this state, be subject to arrest or the service of process, civil or criminal, in connection with matters which arose before the witness's entrance into this state under the summons.