You will enter the state refund from your form 1099g in the year you received it. It is entered under the "Income" tab. Scroll down to "Other Common Income" and you'll find the "Refunds from state/local taxes" topic.
Some or none of that refund may be taxable. If you used the standard deduction in the year for which you are getting the refund, then none of the amount will be taxable.
If you itemized however, some of the amount may be taxable. TurboTax will walk you through those entries to determine the tax, if any.
You may have also received a 1099-INT for the interest. That will be entered in the "Interest and Dividends" topic. That amount will be taxable income.
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