It's probably New York City income tax withheld. Where are you seeing NY CIW? Is it in box 14 on your W-2? There are no rules or standards for the information in box 14, or for any abbreviations that are used. The employer can put pretty much whatever they want in that box. If there is something you don't understand, you should ask the employer to explain it.
City income tax is supposed to be in box 19 of the W-2, not box 14.
