Form 1099-G for what? Unemployment? State tax refund? Paid family leave? Something else? And from what state?
Basically you get Form 1099-G from the government agency that send you the payment. If it's for unemployment or a state income tax refund, some states send the 1099-G in the mail, but many do not mail it. If they don't send it in the mail, you have to access it on the state web site for the particular type of payment.
