The form 1099G is for a government payment. MA employers can choose the state plan or a private plan. The private plan payments can be on a form 1099-Misc. The form 1099-Misc does not necessarily indicate self-employment. The amount reported in box 3 is "Other Income."
Enter the form in the "Wages & Income" section. Scroll to "Other Common Income" and select the 1099-Misc topic. Enter the form information and answer that the pay "did not involve work."