If you itemized your deductions in the previous year, all or some of your prior year state income tax refund may be considered taxable income on this year's Federal tax return (Schedule 1 (Form 1040), Line 10). If you claimed the standard deduction, then the state refund would not be taxable.
If you had a balance due with your 2017 state income tax return or made a 2017 state or local estimated tax payment after December 31, 2017, this may be deductible on Schedule A, Line 5.
Prior year Federal tax refunds (and payments) are not taxable (or deductible) on the current year's Federal income tax return. However, please check with your state to determine if this information needs to be reported anywhere on your current year state tax return.