It sad to say, but him shooting the dog after it was crippled and crawling away is probably the only way they'll see any justice. Courts have consistently ruled that if a dog is advancing on a cop they can kill it, whether or not has any indications of hostility.

Since he shot it three more times when it was disabled and crawling away, they might be able to win a civil case against the city. If the city gave a shit, they could charge him with in animal cruelty violation, but they won't. They'll still break their back bending over backwards to protect a cop, unless they're offering a one up as a sacrificial lamb to screeching minorities.