This is a pretty common scam - actually - many more power companies are reporting that their customers are receiving the same calls too. More info here:
Con Edison Warns Customers: Beware of Con Artists Claiming to Pay Your Bill
Con Edison Media Relations
For Immediate Release: August 23, 2013
11 a.m
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NEW YORK - Con Edison is warning its customers to be alert for scammers posing as company employees promising to lower a customer’s bill in return for cash or a check.
The company has received reports of scammers approaching Con Edison customers in Yonkers, Queens and the Bronx, showing what they claim is a company identification card. Some customers have given the scammers cash or checks.
Anyone approached by someone claiming to be from Con Edison should ask to see identification. If you still have doubts, call 1-800-75-CONED to confirm the person is a company employee. If you think you have been a victim of a scam, call your local police department.
This scam is similar to instances last year where customers were offered discounts or vouchers toward their utility account. The scammer would pay the account balance with a fraudulent checking account and tell the customer the account was paid. The customer would then check the account’s status online or by phone, see a payment posted, and pay the scammer a percentage of the payment.
The scammer then asks the customer to introduce him or her to friends, partners, or others. After a few days, the scammer disappears. Days later, customers learn that the payments did not go through, and that they still owe their original balances.
Con Edison also is warning customers not to fall for a phone scam where a caller says a payment must be made by purchasing a Green Dot Money Pak to avoid having utility service turned off.
These callers are not from Con Edison and Con Edison does not authorize payments of electric or gas bills by pre-paid debit cards such as the Green Dot Money Pak. While many retail stores accept the Green Dot Money Pak for payment, Con Edison does not.
These scammers sometimes even tell customers about a store near their home that sells Green Dot cards. The individual instructs the customer to pay cash to put money on the card, and then to provide the number on the card to the person who called.
Once the customer provides the Green Dot card number, the money on the card is stolen.
Some reports reveal scammers even have made a Con Edison phone number show up on the customer's caller ID.
Be alert if a telephone caller asks you to arrange for any pre-paid debit card as payment for your bill, or to send money to an out-of-state address. Never arrange payment or divulge account or personal information, including debit or credit card information, over the telephone, unless you are certain you are speaking to a Con Edison representative.