My state income tax refund is taxable for federal purposes. NY is asking me how much to allocate to NY resident income (I lived in 2 states) - is it state taxable too?

[DanielV01]

It depends.  Please notice this excerpt from the IT-203 (NY nonresident and part-year resident return):

Line 4 – Taxable refunds, credits, or offsets of state and local income taxes

Federal amount column

Enter the amount you included as income on your federal return. Also enter this amount on line 24, Federal amount column.

New York State amount column

Enter that part of the federal amount that was derived from or connected with New York State sources as a  nonresident. Also enter this amount on line 24, New York State amount column.

Part-year residents

Also add that part of the federal amount that you received while you were a resident. Include this amount on line 24, New York State amount column.  (Italics added).  

If your taxable refund is from NY, it is not taxable to you in NY (unless you were a NY nonresident last year).  However, an out-of-state tax refund could be taxable in New York if you received it while living in NY.