Form W-2G also records your prior year state income tax refund received which may be included in this year's return (if you itemized deductions).
There's no need to add a Form W-2G to your mailed tax return it is not applicable.
The instructions mentioned above were provided examples of the types of forms to send when applicable.
Add any tax forms reporting income received and taxes withheld on your behalf to your income tax return before mailing
[(i.e. Form W-2 box 2 = federal withholding and box 17= state withholding)
(Form 1099R box 4 = federal withholding and box 12 = state withholding)].
