No this is not done automatically.
if you did not itemize on your federal return for 2021, you do not need to enter the amount on your federal return.
However, if you itemized last year and therefore claimed a deduction for state/local taxes you would enter the amount on your federal return as a refund of state/local taxes and it may be taxable.
You may get a form 1099G showing the amount but even if you didn't you would still enter the amount in the same place in TurboTax. In the "Wages and Income" section scroll down to "Other Common Income." In that topic you will find the "Refunds from State/Local returns" interview.
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