Are you sure it's actually being taxed on your New York return? The New York return starts off with a complete list of your federal income, then later it subtracts things that are not taxable by the state. On Form IT-201 the state tax refund is entered on line 4, but then it's also entered on line 25, which gets subtracted when calculating your New York taxable income.
A state tax refund is not always fully taxable on your federal tax return. It's taxable only to the extent that you received a tax benefit by deducting it on the previous year's federal tax return. The calculation of the tax benefit amount is fairly complicated. It has to take into account a lot of factors from the previous year's federal return, including the amount of state and local income tax that you deducted, the amount of sales tax that you could have deducted instead, your total itemized deductions, what your standard deduction would have been if you had not itemized, and so on. You can see the calculation on the State and Local Income Tax Refund Worksheet. Since you are using the CD/Download TurboTax software you can look at the worksheet in forms mode. It will also be included if you save your tax return as a PDF with all forms and worksheets included.
