There are multiple input screens depending on what the 1099-G is for, and you may be on the wrong screen. Try this: click on the Federal Taxes tab, then Wages & Income, then scroll down to the income headings on the lower half of the page (you may have to click "Skip to see all income" to display them).
Scroll to Other Common Income and select the first choice, Refunds Received for State/Local Tax Returns. Then follow the prompts to enter the 1099-G. You'll input the state you received it from, the amount received in 2016, and the tax year the refund was for. TurboTax will ask you a few additional questions, and that's it.
