Can't say for sure, but if you can find city code, I think you'll find that most every town of any size at all has prohibition on shooting firearms in city limits, but few if any counties do, they just rely on judgement calls on nuisance ordinances for doing it in middle of the night, next to churches in session, etc.
Hell, Knoxville even has prohibition on shooting air rifles.
Chattanooga has been cited as an exception to the rule however, and sure enough there's no exact ordinance against it per se, (but the parameters in which you need to do it safely are such that few folks in the city limits would have a property setup to comply), so couldn't say for sure.
Unfortunately, certainly not all city cops necessarily know all the city codes, but seems like this might be one that's straightforward enough you might could trust the answer?
Oh, and seems Anderson County surely doesn't since ORSA and the Norris Range (I think) are both in that county.
Edit: here's link to Clinton City Ordinances, didn't check it out 'cause I'm stuck on slow dialup for a week:
http://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&ved=0CCsQFjAA&url=http%3A%2F%2Fwww.clintontn.net%2FCityOrdinace%2FOrdinaces.htm&ei=4bw7UpeYIOeh4APn_YGwCg&usg=AFQjCNGUS6jfdTxk6g5-aRqTMk41t7c4_Q&bvm=bv.52434380,d.dmg
- OS