You're not allowed to trap owls. Or, kill them, for that matter. They're a protected species, perhaps because contrary to popular understanding, they're one of the stupidest birds extant. Their wide, all-seeing eyes give them an appearance of intelligence that belies their true nature. According to Cornell University biologist Roger Payne, they actually score below chickens. If you've ever been around chickens, you know what a low bar that is.
I had occasion to try to get an owl stuffed some years back. Buddy of mine had hit one with his truck, which surprisingly enough didn't look any the worse for wear even though it took out his windshield in the process. Talked to several taxidermists, and none of them would touch it. Punishment, should they get caught, was too severe. I explained to the ghouls that it had met its end accidentally, but one of the guys I talked to quite rightly pointed out that if they let that go by, all the sudden a lotta owls would suddenly start dying "accidentally", so no. Can't do it.
Another surprisingly protected species? Woodpeckers. They're on the endangered species list, as I suppose they should be since they're such a destructive nuisance pest I'm sure people have been knocking them off as often as possible since time immemorial.