Same situation here, years ago. Some lady in the general neighborhood had a pack of dogs and went along the road with 'em. The yard is pretty big, and the dogs were coming too close - we had a cat that shouldn't be converted to dog food. So my older brother (14? something like that) shot one with a BB gun. A while later, a police car pulls up. The woman said that my mother had shot at her (dog-walker's) with a deer rifle (must've been a silenced model with subsonic rounds, I guess) - then said the shot had missed and hit the dog. Strangely enough, there was no blood on the dog. The officer didn't take anybody to jail. The situation was explained to him, and he believed it and left.
Maybe you should leave a flyer in the mailbox of the people starting the lawsuit - mentioning the penalties for false accusations (must be some). Might scare 'em into honesty. If not, sue 'em.
