Falsely Accused Running Into the Back of a Truck

A month later, the guy never filed a police report, but I am now getting many phone calls from his insurance company who are leaving voicemails regarding the accident. Where does this leave me now? Having to call them back and explain I wasn't at fault and I'm not paying them anything? Further, when they call the guy back that hit my parked car, what would they likely tell him to do? That they can't help him and to sue me for the full amount or partial amount in court? I'm just looking for an answer that clarifies what I'm about to go through. Thanks guys.

If you do not address it, they might choose to sue you. We canot predict what WILL happen. If he made a claim to his insurance company, it is possible they will come after you in court. Or ... maybe not. We can't possibly say.