if done in purpose or because of negligence, yes, although actually going to jail for a single cat-killing is unlikely. Depends on what you actually did.
To kill a cat legally, it must be euthanized by a certified euthanasia technician/LVT/Vet. The only other legal way is a gun shot to the brain in a proper way. And you may not have a cat destroyed that does not belong to you.
Any other method is cruelty to animals and can be a misdemeanor or felony depending on the situation.
If you need your cat killed, most pounds will do it humanely for a small fee. If you know somebody abusing cats, report them. If you're feeling the urge to kill a bothersome cat that's not yours, call animal control if it's causing a legitimate problem. If you're wanting to kill a cat for fun or experience, see a psychologist.