State income tax rates and withholding are independent of federal tax rates and withholding. Your forms W2 have boxes 15-20 that contain the state/local tax information which is used to determine your state/local income tax. Boxes 1 and 2 show your federal income and withholding.
If the amount of taxes withheld (box 17) for the state is higher than your tax liability for the state you get a refund of the overpayment. If the withholding does not exceed your tax liability there will not be refund and if not enough was withheld you would owe state taxes with your return filing.