Bank cards stolen in a burglary in Meltham were used straight afterwards in Saddleworth and Rochdale.
Detectives have now released CCTV images – including an image of a car – in a bid to track down those responsible.
The cards were stolen between 8am and 8pm on Sunday, February 19, at an address in Acorn Drive.
The victim returned home to discover the burglary, and when she contacted her card issuer she was told a number of transactions had already been made.
These took place at a number of shops in Saddleworth and Rochdale.
A car captured on CCTV is believed to have been present near where the burglary occurred, and is thought to be a blue Skoda Fabia.
Det Con Chris Eglan, of Kirklees CID, said: “Returning home to find you have been the victim of crime is understandably very upsetting and distressing.
“Firstly, I would appeal to anyone who may have seen anyone acting suspiciously around the Acorn Drive area on Sunday February 19 to contact police.
“I would also appeal to anyone who can offer any information about the person or vehicle shown in the CCTV to come forward.”
Ring Kirklees CID via 101 quoting reference 13170079644.
