Normally, yes, if it is someone’s pet. To answer the question in the title you have to ask yourself what kind of cat is being killed and how and why it is being killed. Euthanising a cat if the cat is chronically ill is not criminal damage. We know that. Veterinarians do it all the time. It also depends where you are because the concept of criminal damage is based upon ownership of the item being damaged. So, for example, in Australia a person can’t be prosecuted for criminal damage if he or she killed a feral cat because they are classified as vermin in that country.
In fact you can’t be prosecuted for killing a feral cat in any country because they don’t have an owner. But when a domestic cat is owned they are treated under the law as any other item that is owned and it doesn’t make any difference if the item is living or dead or inanimate. Pets are treated exactly the same as televisions. Although there is a gradual change towards acceptance that pets are different to televisions! There is an emotional connection and they are treated as members of the family. Therefore the law is out of date and in need of change.
So killing a domestic cat belonging to another would be criminal damage if there was no good reason (defense) for it under the law. And it would be a minor type of criminal damage called a ‘misdemeanour’ in America because a single domestic cat is relatively inexpensive and of little monetary value particularly if random bred. I suspect that every state in America would classify killing a domestic cat owned by another as misdemeanour criminal damage but I would expect there to be variations across the United States.
There is a good example of this sort of crime reported online in the early part of 2019. It concerns a St. Cloud man (City of Minnesota, USA) who faced a felony charge of animal mistreatment but a misdemeanour criminal damage charge to property. In addition he faced a misdemeanour for not having a trapping licence. He trapped someone’s domestic cat because the cat was wandering into his yard. He trapped the cat in his yard and killed it. Note that the animal cruelty charge is more serious than the criminal damage charge. This is probably because at a fundamental level cruetly to an animal is worse than killing an animal because it creates ongoing pain and distress.
The man is 52-year-old Tim Diederichs. Previously he had used traps to catch cats and returned them to the neighbour but he became upset about faeces in his garden. I cite the example simply to illustrate that killing a cat can be classified, under the criminal code, as criminal damage. Here is a video of the news:
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