A 1099-G for state tax refund does not have any state tax withheld and does not go on schedule W. Only items which have state tax withheld are listed on the schedule W. You should have W2s or 1099s with state tax withheld listed on the sch W. If you did not have any state tax withheld, there would not be a form. Estimates are not included on that form.
If you had state tax withheld on W2 or 1099s and the form is not generating, there is another issue. Are you using online or desktop version?
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