This is a tough situation because she should be prosecuted along with anyone else who files a false report. The problem is that you would have to prove that she knew the information was false when she told it to the police. She might have considered your behavior harassment or menacing and when you went to court, the judge likely decided that it didn't meet that threshold. That doesn't mean that she filed a false report. It's up to the police to investigate and they did and charged you. It's than up to the courts to determine whether the evidence shows a crime was committed.
There's also a concern about chilling the filing of police reports. After all you don't want to file a report and have the person beat the charge only to file charges against or sue you.