No, Federal taxes are not a deduction on either your federal or state tax return.
If you get a refund of Federal Taxes you don't enter them anywhere.
If you get a refund of State Taxes they may me taxable if you got a benefit for claiming them in the previous year and then they were refunded.
If you get a 1099-G from the state then you probably got a benefit that you have to report.
If you don't get a 1099-G, you probably didn't get a benefit and can ignore the state refund.