No, you can't get a deduction on your Schedule A from the state refund that you received in the previous year. The SALT deduction on Schedule A lets taxpayers who itemize deductions when filing federal taxes deduct certain taxes paid to state and local governments. You don't get to deduct your refund on Schedule A.
When you receive a state refund in the previous year and you itemized deductions and deducted your state taxes that year on your Schedule A, your state refund may be taxable on the current year's tax return. TurboTax will do the calculations.
For more information, refer to the TurboTax Help article Do I need to report the state or local refund I got last year? Is it taxable?