While there might be a criminal law provision in your state making it a crime to filea false police report against someone, what you probably rather want to do is to sue in civil court. There is a tort called "Malicious prosecution." There are other torts that might be applicable, too, like defamation, intentional infliction of emotional distress and others.
But before you get your hopes up too high let me warn you: The burden of proof in these cases is pretty high. For malicious prosecution for example you would have to prove that the employer acted intentionally and with malice. That means, he did not have the intention to bring you to justice, for example because he really thought you had stolen something, but he wanted to use this to get rid of you, for example. His motive to bring prosecution must have been improper. Also he must have urged the authorities to prosecute. Just going to the police station and filing a report usually is not enough, since it is in the discretion of the prosecutor's office, to dismiss the charges. The employer would have to actively urge the DA to prosecute.
So you see, unless you have a really strong case against the employer, and very good proof, your chances of succeeding are slim.
The same goes for the other torts: Defamation and IIED also have pretty high burdens of proof to meet and most cases do not reach that level.
