Mandatory reading for police agencies interested in addressing this issue - The Problem of Dog-Related Incidents and Encounters
Half of intentional shootings by police are of dogs.
Police Shootings Of Non-Aggressive or Non-Injurious Dogs
Ogden police shot and killed a dog who barked at them. Link (Other articles indicate the dog is described as a German Shepherd).
This shooting in Regina, Canada could have been prevented had police officers not entered a fenced in, gated backyard without permission. In the pursuit of a suspect, an officer with a canine entered a gated backyard without permission and encountered a 7-yr-old chained dog described as a Pit Bull. Both dogs fought. Another officer shot and killed the Pit Bull. The shooting occurred in a matter of seconds, leaving the owner - 20 feet away - no time to intervene. Police are investigating themselves, so y'all know it will be fair and impartial! Link
Coral Springs police entering a yard without permission shot a dog multiple times, killing him. The dog, described by police as a Pit Bull and by the owner as an American Bulldog, barked at officers. Obviously, they had to pump him full of multiple bullets. Link
An Austin police officer shot a dog, described as a Pit Bull, in the leg when the dog ran at him. Police were trying to get two loose dogs into a patrol car when one ran away or towards an officer. The dog is fine. Link
In a California town I've never heard of but that is in Monterey County, a German Shepherd was shot three times by police and killed. The dog had been taunted by children. He broke down the fence and chased the kids away, resulting in police being called. When police arrived, the dog was back in his yard, having not eaten anyone. When they got too close, the dog ran at them and, for that reason alone, they shot him multiple times. Link
Police Shootings of Dog(s) During or After an Actual Dog-Human or Dog Bite Incident
San Francisco police shot and killed a homeless man's dog, described as a Pit Bull mix. The dog bit the officer, and the officer shot her multiple times. Link
Richmond police shot a dog described as a Pit Bull after he nipped two children. Both children suffered minor injuries. The dog was shot when an officer claimed he charged. The dog is alive. Link
A police officer was forced to shoot at two dogs who were mauling a man. The man had gotten into a fight with someone and in his fervor to flee, he scaled a fence and ended up in a enclosed yard where a mastiff and Rottweiler lived. The dogs protected their territory. When police arrived, he tried to get the dogs to stop but to no avail. The guardian of the dogs was unable to stop the attack. The officer made the decision to injure the mastiff by aiming explicitly for his rear leg and firing off one shot. That one bullet stopped the attack and both the injured dog and human were taken to their respective medical facilities. Link
Classing it up in Warren, where an officer purposely shot a dog, described as a Pit Bull, despite the dog not being a threat to him or her. The loose dog got into a minor scuffle with a leashed dog. When the guardian of the leashed dog interfered, he was nipped on the hand. He was able to keep the dog at bay with a stick. When the officer arrived, he simply called the dog over, shot him with a shotgun, and dumped his body in a dumpster. Like I said, classing it up in Warren! LInk
Police Shootings of Other Animals
When a gate at a wild animal breeding center in California was left partially open, a male lion escaped into his larger enclosure where an intern was cleaning. He swiped his paw, breaking her neck and killing her. When officers arrived, the shot and killed the lion. Link