At around 8.20pm on Thursday 13 December 2012, a woman was walking out of the town centre across the footpath which runs parallel with Stray Rein.
As she walked along, she came across a man stood beside a tree who exposed himself to her.
The victim shouted at the man and he ran off towards York Place.
The victim immediately called the police and officers attended the scene of the incident along with a police dog handler, although the suspect was not located.
The man is described as aged between 20 and 30 years old, 6ft tall and was wearing light coloured jeans and dark coloured heavy boots.
Officers have carried out extensive enquiries in the area and are appealing for anyone who was walking or driving over The Stray on Thursday night who saw a man running off or who witnessed the incident, to contact them.
Detective Sergeant Dave Horne of Harrogate CID, said:
This behaviour is disgraceful and the man must be stopped before he causes any more distress.
Members of the public should be allowed to go about their business without being confronted by such shocking and appalling behaviour.
Anyone with any information is urged to contact North Yorkshire Police on 101, select option 2 and ask for Harrogate CID.
Alternatively you can pass information anonymously to Crimestoppers on 0800 555 111.
Anyone who is subjected to this type of offence should call the police immediately on 999.