Does NYC 1127 tax payment offsets NJ tax liability?

I live in NJ state and work for NYC. employer gave W-2 form, NYC 1127 form, total two forms. Need to file 1)Federal, 2)NY state IT-203(non-resident), 3) NYC 1127, 4) NJ-1040.

Q: Can I add two COJs (Credit for Other Jurisdiction) to offset NJ state tax liability?

(one for NY state tax COJ, another for NYC 1127.2 tax COJ)

 

NYC 1127 is a Condition of Employment tax bill, and form states "NYC 1127.2 Wage and Tax statement" and W-2 form, NYC 1127 has two separate tax withholding amounts. Actually, W-2 box 20A has NYC entry but withholding amount is in NYC1127. Tax situation is "standard deduction".

Can NYC Section 1127 payments, as a condition of my employment with NYC, be claimed as an employee e...