It varies state by state. In Montana you can own them but you have to have a fence of sufficient construction to keep them isolated, it's a lot like (essentially is) having quarantined live stock.
you can hit em as hard as you want, but you have to hit em first
Keep in mind the animals we shoot for food and display are not bullet proof. Contrary to popular belief, they bleed and die just like they did a hundred years ago. Being competent with a given rifle is far more important than impressive ballistics and poor shootability. High velocity misses never put a steak in the freezer.
Ohio is oddly lenient in this regard. There was a big disaster on a private game reserve recently with the release of exotic animals and suicide of the owner/operator. It was a big enough event that it may cause some legislative attention to the subject.