Uh... WRONG!
You can shoot an animal that is doing damage to your property OR being a threat to you.
Otherwise, you cannot.
If I don't want a song bird in my yard and I shoot it, guess what? I just shot a protected animal
that wasn't endangering my property or threatening me... NOT legal.
You shoot a dog in your yard that is not threatening you or damaging your property,
you can be brought up on cruelty to animals charges.
And no, you don't need a permit to fire a gun. You need a permit
to CARRY a hand-gun in public or you need a permit to HUNT on public prop