Quote Quoting Mr. Knowitall
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Under the Penal Code, as linked above, "'Crime' means a misdemeanor or a felony". A violation is not a misdemeanor or felony, and is thus not a crime.
The verbiage of the question suggests they are not concerning themselves with the technical definition of a crime but are speaking to anything the typical reader would consider a crime. Otherwise they would have no reason to exclude with such specificity minor traffic violations.

Maybe if the op would put the question in context it would help him recieve a more applicable response. I realize the title of the thread suggests your explanation may apply but the question itself suggests otherwise. If this is for something such as an application to enter the military or most any security clearance, the technical definition of a crime in New York would be irrelevent.