Well, we are glad you asked. First, our obligatory lawyer stuff. We are not giving you legal advice. This is just a general discussion not specific to you or anyone else. If you need advice about a specific case, then see a lawyer.
Okay, so here are the basics. If you are a competent adult, and you suffer injury in a car crash in New York, you have three years from the date of the car crash to bring the lawsuit by filing it. If you are interested, search New York CPLR 214(5).
The time to bring a lawsuit for a car crash will differ if the driver that hit you was working for a town, city, county, or municipal agency, or the state, and you want to bring a case against those entities. It also will differ if you are suing for a minor under the age of 18, or if the person that hit you leaves New York State after the crash for four months or more. That is why we suggest you consult with a lawyer. If you are interested, search New York General Municipal Law Section 50-e, New York CPLR 207, New York CPLR 208, or New York CPLR 217-a.