Yes swimming in Reelfoot lake is permitted as long as you stay safe and swim at your own risk.
It's best to wear a life jacket when swimming in Reelfoot lake or any other lake just for safety but you can swim without one if you prefer at your own risk though.
You can also go canoeing, kayaking etc in Reelfoot lake as well and it's a very fun place to go to.
There's a lot of things to do and have fun at Reelfoot Lake.
Reelfoot Lake is located in Tiptonville, TN and there's lots to do such as fishing, hunting, bird watching, photography, hiking on nature trails, camping, canoeing, boating, grilling and much more.
I've been to Tiptonville, TN Reelfoot lake a few years ago and it was a good experience and a nice place to fish and hike.
I hope to go there again this summer when I have time off from work.
There's lots of other lakes too out there that you can go to and swim, fish, hike and even just camp out by the lake which is a wonderful experience.