Minor car accident, question on insurance claim.

Hi SD,

Here's the situation, I will try to make cliffs of what happened.

1.) One way street, double parked car opens driver side door while I am already half way across.
2.) Damage to my door, fender, mirror.
3.) He says it was his fault, we discuss options but he goes back into his car and drives away.
4.) His friend comes over and gives me her number to discuss options. (She was not at the scene, driver was parked outside her home)
5.) I called her but she did not pick up so I called the cops.
6.) I was able to remember his plate number and cops tracked him down. He will get a citation for Leaving scene of accident.
7.) I called my insurance company to initiate a claim and they said I'm not at fault.

The driver was able to get my tel. number because I called his friend. He's been calling and giving excuses on why he left. He called his insurance company and his insurance company says that I am at fault. Now he wants to exchange insurance information.

I have already discussed with my insurance company on what to do. They told me it is really up to me if I want to exchange information. I was told that I can get all his information from the police report once it is generated.

Will exchanging information hurt my chances of a claim or should I just wait for the police report? BTW, He has been calling many times and asking to deal with this stuff "man to man".

This is in NY.

Thanks ALL!