Since you did itemize on your 2015 tax return, you should enter your 1099-G related to your state tax refund. Since I was not able to determine if you itemized based on your original question, I just added the information about not reporting the 1099-G because there would be no reporting requirement necessary related to this state tax refund for individuals who it not itemized on their prior year's federal income tax return.
You will just need to enter the 1099-G as you received it and the TurboTax system will determine if any portion is considered taxable in the current year based on your particular circumstances.
