Officers only issued the warning today after the offence happened on October 1.
A lady in her 80s was approached by two men who asked if she needed work doing on the roof of her house.
They requested Â£3,720 from the victim, which was paid, but no work had been carried out at the property in Bromley Road.
Detective Inspector Mark Catney of Kirklees CID, said: “These men targeted a vulnerable elderly lady and requested a large sum of money to carry out some work at her address. The work was not carried out and they have not been contactable since.
“We have been working closely with the victim to provide her with reassurance and assistance with crime prevention and are continuing enquiries to establish if others have also been targeted.
“We would advise people to be cautious when answering the door to anyone they are not expecting. Genuine callers should carry some form of identification and will not mind waiting while you check their details.
“If you are still not sure, do not let them in and report it to the police via 101.”
The first culprit is described as a white man in his late twenties, 5ft 5ins,of slim build, with short hair and spoke with a Yorkshire accent. He said that he lived in Soothill.
The second culprit was described as a white man in his late fifties, 5ft 10ins, of medium build, with short hair, no facial hair and told the victim he worked from home in Bradford. Both of the men were casually dressed.
Anyone with any information about this incident or has experienced something similar is asked to contact the police via 101 quoting crime reference number 13170484301