That is pretty much an excusable shooting. The officer, if he shoots a dog when it is not posing as a threat, is showing himself to be a threat.
If I understand US criminal law, it is permissible to shoot a cop under those conditions as you would with anybody.
Try taking that to court...The only "back-up" you'd get would be when you're serving your 25-life.
Sue the cop, sue the department...But I can't see killing another human over a dog.
But what if you don't actually understand criminal law, as it stands in all 57 states?
Whatever right you have to self defense, it is HIGHLY curtailed when the target of your deadly force is a LEO. The state does not care about your dog, or, if you get down to it, you either. It does care about and is highly protective of LEOs.