Car accident but other person left the scene

So I got into a car accident the other day at a car wash where I was rear-ended. I stayed behind to provide the car wash with my information but sustained almost no damage. The other car involved that left the scene had some damage to its grill, but ultimately left the scene. No police report was filed but the car wash indicated that this person was a member, so they have some of their contact information. I didn’t get a license plate or anything from the video obtained. Should I go make a police report about it even though I don’t have the other person’s information? How does insurance come into play if the other person left the scene but sustained greater damage (and if there’s a chance I may be at fault due to the unique circumstances of me getting caught on the conveyor belt)?