Attorney General Peter Kilmartin repeated a warning about the scam Tuesday. The callers threaten to shut off service unless the customer agrees to wire money or provide their bank account information.
National Grid recently emailed 200,000 utility customers to warn them about the scam.
While National Grid does call customers to notify them about past-due balances, the utility does not demand immediate payment over the phone. Customers contacted regarding a late bill are given the option of paying by check, credit or debit card.