There are very short deadlines to bring a personal injury claim against a city or municipality. You need to bring a claim within 90 days of the accident or your potential claim may be time barred and you could recover nothing.
Whether or not you will win depends on the facts of the accident and your injuries. More information is needed to evaluate the case, but the first step is to immediately have a NY lawyer file an appropriate notice of claim to protect your rights.
The party responsible for the truck must have had a duty to you, which may well have existed here based on the brief statement of facts you posted. Were you a pedestrian? Were you in the truck? Does the city have any immunity from liability?
A negligence or even a gross negligence case requires certain elements of proof. There must be legal damages such as bodily injury to be able to make a case. The injury must be the proximate legal cause of the conduct over which you are suing. And a duty must be owed to you.
Too many unanswered questions here to make any further observations.
You should call a lawyer. Many in your area will provide you a free consulation to discuss in more detail your circumstance. The phone call is a recommended way for you to explore more options you may have including whether more can be made about that truck accident you had.
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