It happened at about 8.30am on Monday, March 18 when a man and woman entered the home of a 92-year-old woman in Stockingate, South Kirkby after pretending to be from the waterboard.
The con artists then stole cash the victim's purse before fleeing in a silver van.
Two days later, on Wednesday, March 20, a woman tricked her way into a house in East Drive, Pontefract at about 3.50pm.
A man then entered but both left after the homeowner became suspicious.
Later on in the same day, a woman was let into a house on Acacia Avenue in Pontefract.
She then distracted the 82-year-old victim while a man stole money from her purse.
Police are treating the three crimes as linked.
-> Police close case after investigation into reports of attempted kidnapping of 10 and 12-year-old girls in KnaresboroughThe woman was described as white, about 30-35-years-old, 5ft to 5ft 5ins tall, slim, with fair hair in a ponytail.
The man was also white, in his mid to late 30s about 5ft 8ins to 6ft tall, slim with dark hair and wearing a light T-shirt.
Police are now warning residents to be vigilant and to look out for vulnerable relatives.
They are asking relatives to remind them that they are under no obligation to let people into their homes.
Detective Inspector Sam Freeman of Wakefield CID, said: “We are linking these three incidents and are currently investigating all the crimes which we think were committed by the same suspects.
“We would ask residents to be vigilant, challenge anyone who comes without an appointment to you home, ask for identification and if in doubt don’t allow them access until you have checked with the relevant organisation.
“For them to ensure this advice is passed onto elderly relatives or persons they may care for and to look out for elderly neighbours. Please also to report any suspicious incidents to the Police immediately.”
Anyone with information can contact Wakefield CID via 101 or the independent Crimestoppers charity anonymously on 0800 555 111.