The incident occurred on York Road between 4.25pm and 4.50pm on Tuesday 18 December 2012, when two teenage girls passed a parked car, which had just driven from Duchy Road.
As they passed the car, the driver indecently exposed himself.
He is described as being aged between 30 and 40 years old with short hair. At the time he was wearing a dark suit and white shirt.
PC David Minto, of Harrogate Safer Neighbourhood Team, said:
This is a very disturbing incident, which is especially worrying as the victims were clearly young girls.
I need to speak to anyone who can identify the man responsible for this disgraceful act. I am also keen to speak to anyone else who may have recently been a victim of a similar offence and has not yet reported it.
Anyone who can help the police with their enquiries is asked to contact North Yorkshire Police on 101, press option 2 and ask for David Minto. Alternatively information can be emailed to email@example.com.
Or call Crimestoppers anonymously on 0800 555 111 quoting reference number 12120212938.