Don't put up with this. Take a few pics of your vehicle showing no property damage and consider a complaint against your ex for filing a false report. Any good attorney could rectify this situation for you.
Until you have seen the police report, it will be difficult to assess what the case is based on and how best to approach it. You should retain counsel right away so that you can figure out how to defend the case. But to answer your question, alleged victims make statements (whether true or not) and the police act on those statements. You need a good attorney to dismantle the case if, indeed, you have no culpability.
Hire an attorney to defend you. They should be able to put together a strong defense for you. Also you should think about filing charges against your ex for filing a false report.
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A hit and run can be charged for someone "involved" in an accident. Lack of damage doesn't end the suspicion, but it certainly makes the prosecutors case harder to prove
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