As a general rule, complaints to law enforcement, if made in good faith, are privileged. If she is making these complaints to the police in bad faith you may have a claim for defamation. Actually, you would start with a cease and desist letter to anyone making these false accusations.
If this does not get a retraction, you will need to file suit for defamation. This cause of action is specifically for damage caused to one's reputation. To establish a prima facie case of defamation, four elements are generally required:
1. a false statement purporting to be fact concerning another person or entity;
2. publication or communication of that statement to a third person;
3. fault on the part of the person making the statement amounting to intent or at least negligence; and,
4. some harm caused to the person or entity who is the subject of the statement.
This involves complex litigation and it is strongly advised that she retain local counsel to assist you in protecting your rights before taking any action in court for this matter. Also, any cease and desist letter will carry more impact on attorney letterhead.
If you need assistance in finding an attorney, contact your state or local bar association. You can also try Martindale Hubble. Many attorneys themselves use this site to locate attorneys outside their jurisdiction or expertise:
It is a huge worldwide database of attorneys searchable by location and specialty.