I don't know if it extends to being on your own property or not, but you can get in trouble if your dog harrasses wildlife of any kind on public land. I.E., you are walking on a hiking trail with your dog and it chases a deer. Of course, you can also get in trouble for picking a wildflower, taking home a pine cone, or even if your neighbor's unsupervised toddler decides to crawl through your fence and climb up your horse's leg while it is standing safely contained in your corral, and the kid gets hurt by doing so.
An interesting question that stems from this...if it is illegal to kill the hawk, what if the hawk is attacking you and you reasonably believe your safety is at stake? They can do some serious damage, maybe even kill a very small child. We have an overly aggressive young Red Tailed hawk hanging around our property that has repeatedly dived at people's heads in an attempt to attack them, and having seen his claws that close to my face...I was really scared! It's weird that he goes after people like that, but does not bother my chickens.