Car Accident Compensation in New York You could be eligible to make a claim on car accident compensation if you've been involved in an accident. You may sue for economic losses in excess of the limits of your policy as well as non-economic damages. But, there are a few factors that may affect the amount of your claim. If you have been seriously injured, you may claim damages in New York. There is a time limit to file an claim for car accident compensation If you've been injured in an accident in the car you could be entitled to compensation.