As recently noted in the news, New York City is apparently plagued with malfunctioning traffic control devices that are governing intersections, particularly in Manhattan. But just because an accident may occur at one of those intersections doesn't inherently mean that New York City, or any municipality in New York, will be held liable for the car accident or pedestrian knock-down as a result.
Consider the 1999 case of Rubinfeld v. City of New York. In that case, the plaintiff sustained very serious personal injuries as the result of being hit by a car as she crossed the intersection of Avenue O and East 17th Street in Brooklyn. Before she began to cross the street, the plaintiff looked at the pedestrian "walk/ don't walk" signal on the northeast corner, and seeing that it "was blank," waited in vain for another "8 to 10 seconds" for the sign to illuminate before concluding that it was malfunctioning, and shortly thereafter, crossed the street after looking in both directions for oncoming traffic. She was then hit by a car in the middle of the intersection.
After a jury held the City of New York 20% responsible for the accident, the appellate court reversed, and dismissed the case against the City of New York, holding that since plaintiff "did not rely upon the signal in making her decision as to when or even whether to cross this particular street. Furthermore, the signal's failure to illuminate, standing alone, did not render dangerous the otherwise reasonably safe condition of the intersection."