The incident took place shortly after midnight on Monday, August 7, by an ATM outside a convenience store in Smith House Avenue.
A man approached the 42-year-old victim and held a screwdriver to her neck, making her walk a short distance down the road with him.
The victim managed to flag down a passing motorist and the man ran off in the direction of Whinney Hill Park.
The man is described as white, around 5ft 10ins tall, aged between 20 and 40-years-old, of medium build, with short, dark hair. He spoke with a local accent.
Detective Sergeant Nick Speed, of Calderdale CID, said: “At this time, the man’s motives are unclear but this is clearly a concerning turn of events.
“I would ask anyone who was in the area around the time of this incident and saw a man matching the man’s description or who has any other information which could help our ongoing enquiries to please call Calderdale CID via 101 quoting 13170361763. Information can also be provided anonymously to independent charity Crimestoppers on 0800 555 111.”