Where I am, if you shoot a hawk you are in for a hefty fine. If you were to say that you shot the hawk because it was killing your livestock and you had proof of this, you might could get away with it. Might. It really depends on the person who finds you out.
It does not matter where you are, you can't shoot a hawk or an owl. You can't kill it even if it is killing your birds....you have to call Fish and Game and hopefully they will send a trapper. It depends on what kind of risk you want to take I guess.
Walt