There are several uses for the 1099-G form, and different places in TurboTax to enter them, the 1099-G for your state refund should be entered here:

• Select Federal Taxes (Personal if using TurboTax Self-Employed or Home and Business)
• Select Wages & Income (I'll choose what i work on)
• You may need to click on Skip to see all income
• Scroll down to Other Common Income
• Click on Show more and Refunds Received for State/Local Tax Returns
• Start or Update