E.W.
My advice is two fold: First, Kill her with kindness. I, too, had neighbor like that. She didn't go as far as calling the county, but we were harassed on a daily basis. So I started speaking to her to when I ran into her. Nothing much, just a hello, how are you. I also gave her baked goods whenever I baked. My husband offered to help her with her computer, and my daughter would color her pictures that we left on her stoop in pretty homemade cards. She didn't know what to think about me or my family. She's backed off and now we no longer have a problem w/ her. She's actually one of our best neighbors now. :-)
Failing that, document every time she harasses you or your family. Keep a journal by the front door and write it down. Be sure to put dates and times. If she calls the officials on you, write that down as well. (Make sure to get copies of the incident reports!) After a few months or when the journal is full, take her to civil court and sue. If you can, try to get the incidents on video tape. Video surveillance is relatively cheap now. It doesn't take anything to pop a camera in the front window or some other place where you can monitor your property. You have a right not to be harassed. CPS won't tell you who called, but they do keep records. Too many false reports and she will eventually hang herself with them, if she is leaving her name, if not, by your documenting the incidents, I'm sure you can reasonably prove that she's the one doing it.
I wish you luck and hope you go with option one and that it works. She may just be lonely, jealous, and not know how to reach out to people.