If you have a permit you're probably good. Most state parks recognize a carry permit. Better to ask forgiveness than permission. Lol.
I copied this from the TDEC website. 0400-02-02-.11 FIREARMS, TRAPS, AND OTHER WEAPONS. (1) In park, natural, and historical areas the use of traps, seines, handthrown spears, nets (except landing nets), firearms (including air and gas powered pistols and rifles), blow guns, bows and arrows or crossbows, and any other implements designed to discharge missiles in the air or under the water which are capable of destroying animal life are prohibited. The possession of such objects or implements is prohibited unless they are unloaded and adequately cased, or broken down or otherwise packed in such a way as to prevent their use while in the park areas.
I looked on a couple of websites and can't find an answer. You may need to call them.
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