Yes, you will file a NY nonresident return for the income you earned in New York.  Unfortunately, because it seems that your staffing agency did not withhold NY state tax, you will have to pay NY for the amount of income you earned in NY.  However, you will also receive a credit on your Connecticut return for the amount of tax you must pay to New York on that income, up to the amount that Connecticut taxes the same income.  This is done to reduce the negative impact of double-taxation.