You're attempting to do something extremely difficult at best. The fact that the charges were dropped doesn't really help, as for most matters you need to be acquitted entirely of charges before you can make a real case for such things as malicious prosecution. All that a preliminary hearing determines is whether there is enough evidence to take the case to trial -- a lack of evidence is not legally the same thing as proving that the report was false.
If the police don't charge the alleged victim with false reporting, you will have to attempt a private case through a magisterial district judge (what used to be called a district justice here in PA). A private civil suit will be hard to maintain given what I told you above. If you had been acquitted you would possibly be able to make out a criminal case for malicious prosecution, but if the police would not charge her you would have to file a private criminal complaint -- and all private criminal complaints are reviewed by the District Attorney, who can block their proceeding.
I would check with an attorney who could be given all of the details in the matter, but you're not in a good position based on the information provided.