A permit is necessary to take, harm, harass, trap, or kill any wildlife with few exceptions.* Squirrel isn't an exception. Squirrel season is in the summer.
Exceptions that can be killed by any method unless specifically prohibited are Norway rats, black rats, house mice, coyotes, armadillos, groundhogs, beaver, freshwater turtles, venomous snakes, frogs, salamanders, fiddler crabs, fresh water crayfish, freshwater mussels, and nutria (I had to look this one up - it looks like a small capybara).* I thought hogs were on the list too?
Then again, who's going to know? This trap looks dangerous to cats though.
Thanks for adding traps to my list of stuff to stock up on. I took the * info from a GA Master Gardener Handbook.