State tax filing

You can deduct the amount you pay each year to state or local governments for licenses and regulatory fees for your trade, business, or profession. (Italics added)

You can deduct an occupational tax charged at a flat rate by a locality for the privilege of working or conducting a business in the locality. If you are an employee, you can claim occupational taxes only as a miscellaneous deduction subject to the 2% limit; you can't claim them as a deduction for taxes elsewhere on your return. (Italics added)

While NYC claims this is not a tax, their own definition "Section 1127 of the New York City Charter is not a payment of any City tax, but is a payment made to the City as a condition of employment..." (direct quote from the NYC Section 1127 Form) is remarkably similar to the IRS' definition of the Occupational Tax:  "charged at a flat rate by a locality for the privilege of working or conducting business in the locality." Still, if the Section 1127 payment is not an occupational tax, then it most certainly fits the definition of a fee.  

Either way, the amounts are deductible, not as city or local taxes, but as unreimbursed employee business expenses, which are subject to 2% of your AGI (and itemized deductions).   In most cases, these expenses are claimed on Form 2106 or 2106-EZ.

{Edited 3/27/18:  19:45 PST}