My side mirroir collided with the side mirroir of an illegally parked car. the owner of the parked car and I exchanged driver license information but we didn't contact the police to fill up a report. His insurance company has contacted me regarding the accident. What should I do next? Should I resolve this in private and no involve insurance company so that it won't leave a record in my file, what is the next step. It a report is not filled, can the illegally parked driver still claim dommage from me?

Depends on how much his insurance company is asking for. If it is minor damage and you can pay out of pocket, you can resolve it without involving your insurer. This way your rates should not be affected. As the driver has already filed a claim, his insurance company can come after you for the damages. If it was just the side mirror... personally I'd just write them a cheque.

That said... if they're suddenly saying that the car has all sorts of damage here and there... maybe you'd be best to get your insurance company involved. Your rates will be affected but it might save you a lot of trouble.

Would I still be able to settle without involving my insurer even when the other party has involved his insurance company? What kind of document or agreement would I need to obtain to make sure that they won't be coming after me again?

I don't see why you couldn't just settle with them, if it's a minor incident.

If you're worried about additional action, you could just ask them to send you an agreement that you'll pay the requested amount in exchange for that being the final action taken by them... although that's really something that I'd rely on my insurance company for, if it were me.