Severn Trent Water is warning customers after some were asked to disclose bank details by bogus employees.
Customers have been contacted by conmen claiming to be from the water company after last week's announcement Severn Trent will refund customers after a £42 million price gaffe.
Every Severn Trent customer will have a rebate, of £3-£4, over four years after what the industry watchdog Ofwat described as "poor internal processes and controls" led to overcharging.
Jonathan Bailey, Severn Trent customer relations director, said the refund would be paid into customers' accounts and they would not be contacted.
He said: "We will not call customers and ask for any details or arrange a visit to discuss the refunds. Customers should be very suspicious of anyone asking for account details."
Police said conmen use a variety of techniques to convince people they are genuine. People worried can register with Severn Trent for an individual password, which only employees will access.
In addition to the rebates Severn Trent is setting prices £7 million short of the recommended level over the next two years.