‘Homicide’ refers to the killing of one human by another.
I doubt anyone has been charged with homicide for shooting a dog, even if it’s a police dog.
Suppose the dog is trailing a suspect, and its handler is 100’ yards behind it. If the suspect is “detained” by the dog, does it just get to chew on him while the officer catches up? Can the suspect defend himself in the interim? Would his instincts toward self-preservation be criminal?
Dogs aren’t people. We had one locally that caught a couple of porcupines while out tracking suspects. I don’t trust its judgement.