In order for the state attorney to prosecute a perjury case, the prosecutor will have to be able to prove that the person knowingly lied. This is extremely difficult and usually the police/prosecutor will not file perjury charges on someone simply because another person said that person lied. If it can be proven it was a lie (for example, you can prove that you weren't even in town when the allegations occurred or they admit to lying) then the state attorney would more likely file charges. Perjury is extremely hard to prove.
This is not to be considered legal advice nor does an attorney-client relationship exist.