The W-2 shows how much state income tax was withheld from your paycheck, it does not tell how much you are supposed to pay state income tax. To figure out how much your state income tax is, you need to prepare your state income tax return using the tax form. If you use TurboTax, all the information you entered in the federal section will flow to your state section, there should not be much left to prepare your state income tax return.
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