The man was involved in an argument with two other men on bicycles in Church Avenue, at about 2.30pm on Friday.
Police have today (Monday) appealed for witnesses after bystanders said they saw the man reveal a knife during the altercation.
A North Yorkshire Police spokesman said: "We are requesting the public’s assistance to help establish the full circumstances surrounding the incident."
They added: "Witnesses have stated they have seen the man reveal a knife from his waistband and shown it to the two men on the bicycles."
The cyclists rode off on King Edwards Drive, and the other man made off on Church Avenue, towards Bilton Lane.
The man is described as being slim, with black curly hair and an olive complexion.
He was dressed in a black jacket, black trousers and black shoes.
Anyone with information is asked to contact police on 101, quoting 12180096695.