It happened at the Ultimate Outdoors store on Coach Street at about 5pm on Saturday.
A man entered the store and removed items of clothing from a display before leaving without paying.
In its appeal, the force said the culprit was chased by staff and the goods were returned before he ran off again.
The man police want to speak with is is described as being white or Asian, aged between 30 and 40 years-old, about 6ft tall with dark hair and a beard.
He had a blue outer jacket on with blue jeans, a grey long-sleeved top and a blue baseball cap.
Anyone who recognises him is asked to call 101.
Quote the North Yorkshire Police reference number 12180046299.