The 21-year-old woman was walking along Commercial Street at around 10.30am on Tuesday when a man approached her from behind before taking her purse.
Before the incident the suspect had been sat in the driver's side of a black Ford Focus parked outside the HSBC bank.
After stealing the purse, the suspect ran back to the car and drove off at speed towards George Square.
He is described as a white man, wearing a dark coloured hooded top, grey jogging bottoms and blue trainers.
Detective Constable Walsh of Calderdale CID said; "I would appeal to anyone who may have been in that area of the town centre on Tuesday morning, and may have seen the suspect and or the vehicle described to come forward. Equally, anyone who may have witnessed the incident taking place or who has any other information should speak to police. Enquiries are ongoing."
Anyone with any information is asked to contact DC Walsh at Calderdale CID via 101 quoting 13170002715.