You only need to include in your federal income a state or local tax refund (usually reported in Box 2 of Form 1099-G), if you had taken a deduction on your federal return for paying those state or local taxes in a prior year. Box 3 of Form 1099-G will indicate the relevant tax year.
To enter your Form 1099-G information into TurboTax, please see the following TurboTax FAQ, "Where do I enter a 1099-G for a state or local tax refund?": https://ttlc.intuit.com/replies/4768356