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TWEO thieves posing as police officers stole £155 from a 90-year-old woman at her home in River Drive, Strood.
The pair told her they were officers from CID making inquiries about burglaries in the area.
Claiming he wanted to make sure her house was secure, one man went into the house and appeared to start checking the windows. He was joined in the living room by the second man and then both men left the house.
After they had gone the elderly woman discovered that £155 had been taken from her handbag in her bedroom.
Police have issued descriptions of the two men. One is white, aged about 30, and about 5ft 10in tall, He is slim and was dressed in black.
The second is described as white, aged between 30 and 39, 5ft 4in and also dressed in black.
A police spokesman said: "We would urge all those people living on their own to always ask to see identification if someone calls at your home without an appointment. If you are still not sure call the company they are from using the number from the telephone directory."
Anyone with any information about the crime should call police on 01634 884252 or Crimestoppers on 0800 555111.