That depends on why the state refund was offset--and you have not mentioned the reason. Sometimes the IRS will offset a federal refund for a state debt owed. TurboTax never knows about offsets to your refund, so we cannot say what will happen.
https://www.irs.gov/uac/tax-refund-offsets-pay-unpaid-debts
Reduced Refund https://www.irs.gov/taxtopics/tc203
NOTE: You can contact the IRS Treasury Offset Program Call Center at 1-800-304-3107 to ask if they have an offset for you on file. TurboTax would not have that information.
https://turbotax.intuit.com/tax-tips/tax-payments/who-can-garnish-an-income-tax-refund/L7cPPzDyc
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**