Officers were called to the Fraser Hart shop, in Coney Street, at about 8.30pm on April 1.
Two men got into the store via the roof of an adjacent property.
They made a hole in the wall between the first and second floors of the building, but fled empty-handed when the alarm sounded.
North Yorkshire Police said they also caused damage to a neighbouring Cancer Research charity shop during the attempted burglary.
The force today (Thursday) release CCTV images of two men they are trying to trace in connection with the offence.
Investigator David Pegg said, from the force, said: "These two men paid no regard to the damage they caused to two buildings and the distress they have caused to the staff of both stores. They were only concerned with their own selfish gain.
"Whilst we realise that the CCTV images do not offer views of either men's faces, it's hoped that their distinctive clothing may be recognisable and enable someone to offer information which would assist our investigation.
Anyone with information is asked to call police on 101.