Its legal here in Michigan to kill a dog chasing deer, livestock etc but police don’t encourage it. Both of which can be prevented by not letting dogs run loose.
Sounds like the police had already been called about the dogs.
When I took the hunter safety course many (many) years ago in NYS the DEC guys told us that his was more intended for the feral dogs that were harassing deer. IO asked how you could tell the difference between feral and domestic. He replied that off the record if it was chasing a deer it would be coyote food.