Is it possible that you let your cat out and it went into the neighbor's yard first, and then the dogs chased it out of their yard into your yard?
do you or your neighbor have a fence? if so, what kind? chain link or solid wood (non-see through)?
It just seems like we don't have all the facts here.
I do know that pit bulls are a very aggressive breed of dogs (this coming from an owner of two German Shepherds). But, I'm also a lawyer by training and would be very reluctant to start ANY legal action again a next door neighbor unless it was the absolute last resort and all the facts, or at least most, were completely in my favor and mostly verifiable. Your best course of action, or course, is talking with them in a calm manner about the issue and finding a solution that works the best for all of you. Unless your cat sustained injuries more than $10,000 in most jurisdictions, or she/he passed away, you'd most likely be in small claims court. Most attorneys would not take your case, imho, sadly because of the small dollar amount (yes, I know that's a sad problem of my profession, but just being honest about most of the attorneys that I've met/went to law school with...). You would be out filing fees in small claims court, time to adjudicate (ie, taking time off work), time, etc). And yes, it's the principal of the issue, but I really, really hope for your sake and sanity that you can resolve this with your neighbor through discussions without elevating it to legal action.
If your relationship is even a little strained with your neighbor before this happened, wait until you add a law suit into the mix
