The legality of killing a cat is up to the state laws. Here in GA you can kill any animal that is causing damage or injury to a person or property.
OCGA 16-12-14
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"A) Defending his or her person or property, or the person or property of another, from injury or damage being caused by an animal; or
(B) Injuring or killing an animal reasonably believed to constitute a threat for injury or damage to any property, livestock, or poultry.
(2) The method used to injure or kill such animal shall be designed to be as humane as is possible under the circumstances. A person who humanely injures or kills an animal under the circumstances indicated in this subsection shall incur no civil or criminal liability for such injury or death.
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My personal opinion on outdoor cats is, if you live in a subdivision or close to others, don't. Your cat is going to get on their stuff and that is rude and opens you up to liability for fixing damages. (If your cat slides off my freshly waxed car and leaves claw marks, we're going to have a discussion and you're going to be paying me to fix it.)
Also, outdoor cats do a good job of cleaning up rodents, but they also hunt for fun and are the reason some bird species are being threatened. This is from a study UGA did several years ago.
KittyCam stills showing a captured chipmunk and an injured pheobe, National Geographic KittyCam Program (Washington, D.C., August 6, 2012) A new study of house cats allowed to roam outdoors finds that nearly one-third succeeded in capturing and killing animals. The cats, which wore special video...
abcbirds.org
More fun reading from across the pond:
Officials in New Zealand say it will protect the local eco-system, but the plan is controversial.
www.bbc.com