get a dog, the cat wont come near your house. dogs typically dont bother any other animals except cats. we let my dogs out front to run around at night and they chased a cat and cornere it and nearly killed it. (about 5 dogs)
if you harm that cat, ie shoot with pellet gun, paintball, gun etc.. you can get in BIG trouble if you get caught.
i take it you dont watch animal planet. i have a 3 year old so its on pretty much all day. they have a show called animal cops which is often based in Michigan (location changes like COPS tv show). they arrest people all the time for doing stuff like this.
I dont condone people letting their cats run around free but i dont really care either. in my townhouse complex people do this. i leave my sliding door in my patio open to let in fresh air (need a new screen door). i fell asleep on the couch and i woke up, turn my head over, and Morris the cat is sitting there staring at me, IN MY LIVING ROOM!

this damned cat has tried to do this a few times.
i dont reallly care though i just try to scare him from coming back. i understand people like to let their cats out to stroll around. cant take em on a leash and i never heard of a cat mauling anyone which is why youre not supposed to do this with dogs.
basically, i hate cats myself, but think really good and hard before you decide to do something. can you imagine being fined $1000 by the ASPC(?) or going to jail for a year for a stupid cat?