Elderly residents in Snettisham and Dersingham were targeted by bogus callers who claimed to be from an alarm company working for the police.
Two residents in Snettisham and one in Dersingham received calls from a withheld number last Wednesday morning.
The caller asked about security measures at the home and offered to visit the property to discuss crime prevention methods.
A similar call was received last week by an elderly resident in the Downham area.
Police are once again strongly warning residents not to give out any details about their home security, either on the phone or in person, to unexpected callers and always ask to see some form of identification.
Any suspicious activity should be reported to police using the non-emergency number 101 (calls cost 15p), but if a crime is in progress always dial 999.