Derbyshire Constabulary was first alerted to the phone scam last week but said that, since then, more residents have fallen victim.
The force is now urging people to share the warning with friends and family, particularly those who are older as they are typically targeted.
It said that fraudsters have been contacting people within the postal code areas of DE22 and DE56, claiming to be a DC Matthew Phillips, PC Christy or Sergeant Atkins from a police station in Derby.
A Derbyshire police spokesperson said: "They already know personal details, such as the resident’s name, address and basic banking details.
“The victim is asked to stay on the line and dial 999 to verify the identity of the ‘police officer,’ however someone will answer the call pretending to be from Derbyshire police and will then verify the caller.
"Due to the fact the victim is asked to stay on the line and dial 999, the original call is never terminated and they remain in contact with the fraudster at all times.
“The caller goes on to say that he is investigating the unauthorised use of that person’s bank card at local stores such as M&S and Asda. The use of locations that will be familiar to the victim makes the call appear more genuine.
“Secrecy is the key and victims are advised they should not tell anyone about this call as it may jeopardise the police investigation.
“We know that this type of call can be linked to courier fraud.
“This means that victims will be encouraged to withdraw funds from their bank accounts or Euros from local bureau de change to give to a courier, arranged by the ‘police officer’ making the call under the guise of ‘assisting with a police investigation.’”
Police will never ask for banking information or request that you withdraw money to aid an investigation.
If you receive such a call, hang up immediately, wait five minutes and ensure you can hear a dial tone before calling 101.
You should also contact your bank and make a report to Action Fraud on 0300 120 2040 or online via www.actionfraud.police.uk.