I assume that this 1099-G is a refund of state income taxes for Rhode Island?
Go to Federal Taxes->Wages & Income->Other Common Income, and look for "Refunds Received for State/Local Tax Returns" to start the interview.
If the 1099-G is not for a refund of state income taxes, then go to the next line: "Other 1099-G Income" to start the interview.
Note that your state tax refund may or may not be taxable, depending on the facts and circumstances. Please answer the questions that TurboTax presents; the software to trying to see if your refund is, in fact, not taxable.