New York State - Question about how to handle W2 Box 20 with "1127" displayed

Hello,

On my W2, I have a box 19 (local income tax) amount listed and "1127" listed in box 20 (locality name).

I entered "1127" in box 20 in Turbotax.

 

Since my income was taxed in NYC, I chose "New York City" as the locality in this part of the interview:

 

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The amount is added to my total NYS payments on line 63 of IT-203, which increases my refund.

I work for the NYC government (NYC Hospitals Corp.) within the city. However, I live in Connecticut. Did I input this correctly?

 

I am asking this because NY state sent me a letter stating that the W2 amounts I entered for their taxes do not agree with what was reported to them. They need a copy of my W2.

 

Did I make a mistake, or did my employer?