I posted this story a couple of years ago and got BLASTED by the members here....... But, I know it is true, so here goes.....
A hawk squeezed himself through an opening in my daughter's hen house to attack a hen. He wounded her on her head a punctured her breast in a few places. Then the Araucana/Game cross rooster attacked him. The hawk had an eye injury and a broken wing when we threw a shirt over his head to capture him. When I called the DNR I was told since he attacked chickens and his wing was broken to go ahead and humanely destroy him. I was told to call them back after the deed was done.
Of course, all the grandchildren started crying so I called DNR again and they gave me the number of a rehab facility. The folks from the rehab facility did come pick him up, they also confirmed that Hawks killing chickens can be destroyed. BUT, it is illegal to dispose of the body, it must be turned over to the DNR.
Keep in mind, we did not SHOOT the hawk, we actually caught the hawk INSIDE the chicken house, maybe that is the difference.
My advice is call DNR and arrange a meeting with an officer and discuss your hawk problems.
That is pretty close to my approach. Dogs do most of the apprehending and that is largely with owls (same difference). Female dog outside right now working on a couple of GHO;s being nuisance in cockyard. This dog appears to have developed a technique that got her close to owls on more than one occasion and these young owls have a little more than average stupid going on. We did catch a Barred Owl two years ago although that was released by me despite protests of dogs. They really wanted to munch it like they do raccoons.