Two tracks that move separately
Leaving the scene of an accident without stopping and exchanging information is an offense in New York, and its seriousness rises with the severity of any injury. When only property was damaged, leaving the scene is generally a traffic infraction rather than a crime, though it can still carry license consequences. A civil settlement with the injured person or their insurer can compensate losses, but it does not by itself dismiss a criminal charge, because the prosecutor and the court decide the criminal case. Restitution and the injured person's views can still be relevant to how that case is resolved.
Insurance and communication
Most hit-and-run claims are paid through insurance, either the driver's liability policy or the injured person's own coverage, and insurers usually require prompt notice of an accident. Notify your insurer without delay, ideally after a short conversation with counsel about what to say, because statements to an insurer can reach prosecutors in some situations. Do not contact the injured person or their family directly to offer money or explain what happened. Gather your policy, photographs of the vehicle, and any messages about the incident, and talk with a lawyer before repairing a vehicle that investigators may want to inspect.
First steps on either side
For a driver, we start by finding out whether a criminal case or investigation is open, whether police have identified the vehicle, and which insurers have been notified. If no one has contacted you yet, coming forward promptly through counsel is one of the most important early steps, since the law expects drivers to report. For a person hit by a driver who fled, New York's no-fault system and uninsured motorist coverage may provide a route to compensation even if the driver is never found. Those claims carry notice requirements that can be short, so reporting the crash to police and your insurer quickly matters.