6-54-301 is the "one-mile" stuff.
Can't find an email address for one of the law instructors, but I got into a conversation with another officer who is a little closer to remembering the academy days than myself. He said the way it was explained is this- TCA 40-7-101 says that arrests may be made by the following persons; (1) an officer with a warrant, (2) an officer without a warrant, (3) a private person. Officer is defined throughout TCA (person employed by any municipality or political subdivision of the state of Tennessee whose primary responsibility is the prevention and detection of crime, and the apprehension of offenders). There's no exclusion to an officer's powers of arrest under 40-7-101 based on jurisdiction, on or off-duty status, etc. Therefore, it's generally considered that the lack of restrictions is legislative intent to allow LEOs to retain powers at all times and in all places within the state.
Makes sense to me. If you look at White V. Revco Discount Drug Centers Inc. (2000), the court ruled that in Tennessee, police officers have the "full panoply of 'official' police powers even when they are off-duty". This case was in regards to a Knoxville officer making an arrest while he was off-duty. Not quite the same issue we have at hand, but it falls under the same general umbrella of criminal procedure.
This reminds me of people coming to the forum to ask "where in state law does it say I can carry a gun into a bank?" Well, it doesn't, but it doesn't say anywhere that you cannot. Kinda the same situation. Nowhere in TCA does the legislature seem to restrict police powers for LEOs. One might argue that the "one mile" rule hints to it, but then again, the law never refers to officers, but to the powers of the municipality itself (municipal courts hearing cases, collecting fines, etc.?).
One thing we can all agree with... clearer TCA would be great.