It occurred at around 9.30pm on Monday 3 September 2012, in the Duchy Road area.
A 27-year-old local woman who was walking down Clarence Drive when a car travelling in the opposite direction stopped. The man driving the small dark car approached her without speaking, before making an obscene gesture. The man did not speak or make any attempt to touch the woman.
She shouted at him and he returned to his car, driving off towards Duchy Road.
The man police need to trace is described as white aged between 35 and 45, around 6ft tall with a broad build and a shaved head.
Police Sergeant Andy Stow, of Harrogate Safer Neighbourhood Team, said:
If you can help to identify the man who approached the woman I urge you to come forward and contact the police or Crimestoppers as soon as possible.
I am also asking the man to come forward so that he can explain why he behaved in this wholly unacceptable manner.
I know that there have been a number of posts on social networking sites regarding this incident. I want to reassure people that we have not found any evidence that the man had any other intent than making the obscene gesture.
Anyone who can help to identify the man is asked to contact North Yorkshire Police on 101, press option 2 and ask for Harrogate police.
Or call Crimestoppers anonymously on 0800 555 111 quoting reference number 12120147312.