Between 1.40am and 1.50am on Saturday, December 30, a man entered Bluebird Care West Dorset in Bridport Road and stole a bank card.
The bank card was subsequently used to carry out fraudulent transactions in the Poole area.
Officers investigating a burglary in Dorchester are appealing for anyone with information to come forward to help identify the suspect.
Police Sergeant Anneka Stone, of Dorchester Neighbourhood Policing Team, said: “Our enquiries are continuing and I would like to hear from anyone who saw or heard any suspicious activity in the area around the relevant time.
“I have obtained a CCTV image of the suspect and while I appreciate it is not the best quality, I am hoping the image may jog someone’s memory to help us identify the suspect.”
Anyone with information is asked to contact Dorset Police at www.dorset.police.uk or by calling 101, quoting occurrence number 55240000510.
Alternatively, independent charity Crimestoppers can be contacted anonymously online at Crimestoppers-uk.org or by calling Freephone 0800 555 111.