The incident took place on the Faverdale Black Path, near Minors Crescent, when a woman was walking home along the upper part of the path on Sunday (January 5).
She was then threatened by a man with a knife, who demanded money from her – but when she refused to hand anything over, he ran off down the steps to the lower path and out of sight.
Thankfully, the woman was uninjured but has been left shaken by the incident, which took place at around 5.50pm.
Durham Constabulary has launched an investigation into the incident, with officers wanting to speak to anyone who may have information to assist the probe.
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The suspect is described as a young man who was wearing a grey tracksuit and a dark mask around the bottom of his face with his hood up.
He was also carrying a Sainsbury’s carrier bag.
If you have information, call the force on 101 with any information, quoting crime reference number CRI00590520.
Information can also be passed on anonymously to Crimestoppers on 0800 555 111.