First, you can be reported for allowing your pet to roam free and you may be cited by the city. A neighbor may make a valid complaint for an animal running free on their property.
Second, your neighbor could be charged for intentionally killing a domestic animal under Minnesota Statutes 343.21.
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I agree with my colleague. Your cat has trained you to let him out - he doesn't "need" to go outside. You can either wait him out or you can take your chances letting him out. I'm not suggesting your neighbor would be justified in killing the cat - just that you have a pretty simple solution to the problem.
If we do not have a signed fee agreement I am not your attorney and this is not legal advice.