They were caught on camera in the R S Marsden Pharmacy, Leeds Road at 1.45pm on Monday 30 April 2012 and again at 4.30pm the following day, Tuesday 1 May 2012.
It is believed that the suspects entered the store together, before taking several hundred pounds worth of cosmetics.
PC Janine Walker, of Harrogate Safer Neighbourhood Team, said:
I would like to speak to anyone who recognises either of the people caught on camera and ask that they contact the police or Crimestoppers as soon as possible.
I am also appealing directly to the couple caught on CCTV. If there has been a misunderstanding and they are not responsible for this theft, I ask them to contact the police immediately so that they can be eliminated from our enquiries.
Anyone who can assist with this enquiry is asked to contact Harrogate police on 101, select option 2 and ask for Janine Walker.
Or call Crimestoppers anonymously on 0800 555 111 quoting reference number 12120069567.