Before you start doing a happy dance you need to figure out if they are wrong or you and why ... carefully review the notice and your return to see who is incorrect.   Then if you itemized deductions the federal return may need to be amended if you were wrong.

Could you have had state tax withheld on some other form besides a W-2, such as a 1099-series form or a Schedule K-1? Check all your other forms.

Your state withholding will not affect your federal tax unless you are claiming itemized deductions on your federal tax return. If you do have itemized deductions on your federal return, the additional state withholding might reduce your federal tax.