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 1). If you claimed the standard deduction, the state refund is not taxable.
If you had a balance due with your 2018 state income tax return or made a 2018 state or local estimated tax payment after December 31, 2018, 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.