No. You do not enter last year's federal refund anywhere. If you got a state or local refund it may be taxable income on this year's federal return.
A State Tax Refund is taxable if you itemized deductions on that prior year's federal return and took a deduction for state income taxes instead of the sales tax. You got a deduction benefit for it so now you have to include it as income. If you took the Standard Deduction it is not taxable and you don't need to report it. Check your 1040 line 12 to see which deduction you took.
