New York State follows a strict statute of limitations for car accident injury claims. If you fail to file a legal claim before the statute of limitations runs out, you are likely to lose the ability to take any action. All motorists in New York must purchase no-fault insurance coverage. When an accident occurs, their initial claim is against their no-fault policy. The policy benefits apply regardless of who caused the accident. However, you can file for a personal injury claim directly against a negligent driver a trucking company, or any other fault party in certain situations.