I'd let your insurance agent know. He may know who insures that idiot. The average cost of a dog bit claim is about $12k and if it is a pit bull it is $24k. If the dog seriously injures a child it is going to ruin an insurance companies year and be in the hundreds of thousands of dollars. WE have a child who got a face scare and it was nearly half a million claim in the end. Juries do not like belligerent Pit Bull Owners. Although we love animal lovers in general once you become belligerent ignoring requests and warnings you become the bad guy.
Let his insurance company handle him.
I would also write a letter to the police, zoning, animal control and the local newspaper and TV news. Let them put pressure on the city/county sheriff and the guy.
Thing is after everyone is noticed "in writing" now if something happens peoples heads will roll. Belligerent dog owner, neglectful sheriff, city counsel who did not ensure sheriff did his job, dog catcher for not catching the nuisance dog which was repeatedly not leashed.
The municipal mindset is that if you do not put it in writing you are just a complainer. 911 get hundreds of ridiculous calls. But if you are a "Document-er in writing" you get a lot more respect.
If you really are concerned for yours, your cats or your neighbors health then you should have an attorney send the letters and notices. When animal control or the police get a letter from an attorney about an issue it becomes something that is not going away and cannot be pushed under the carpet.
These guys get hundreds of silly complaints a week from ridiculous people. A letter from your attorney raises your letter to a much higher elevation.
You do not know when and how this is going to end so start building your journal and case now. Daily documented journal will go along way with a jury when and if a little girl gets a scared face.
PS $20 gets you all the arrest records on a person. If this guy is on parole you can call his PO and get it resolved quickly.