If you want to fill out an accident report or request a police report on the accident, I suggest that you contact your local police agency. In most jurisdictions you can file an accident report after an accident occurs. The NYS DMV site notes that if the property damage of any person is $1001 or more, all the involved drivers of an accident must file a Report of Motor Vehicle Accident (form MV-104). This form must be filed no more than 10 days after the accident. The DMV can suspend your driver license if you fail to report an accident.

As for filing a police report if the other person decided not to personally pay for your damages, it is unlikely you could do so since it would be considered a civil matter which you could pursue the other person in court to seek a judgment for your repair costs. To find out for certain if a police report could be made check with your local police agency.

Before taking the other person to court though if they have insurance on their vehicle you should be able to place a claim against their property damage liability coverage (with their insurance company) for the damage they caused to your car.

For a New York City auto insurance quote, follow this link.