North Yorkshire Police said extensive enquiries had been made to try to find Shaun David Shepherd, but he has evaded arrest.
They want to speak to him in connection with the ongoing investigation into an assault and criminal damage.
Mr Shepherd, 27, lives in Nelson Street but also has connections to the Eastfield and East Ayton areas.
A spokesman said: "Since May 14, officers have carried out extensive enquiries to try and locate Mr Shepherd and are now appealing to members of the public who may have seen him or know where he is now, to contact them."
Anyone with any information is asked to contact North Yorkshire Police on 101, select option 1 and pass information to the Force Control Room.
Information can also be given anonymously via Crimestoppers on 088 555 111.
In the case of an immediate sighting, the public are being asked to call 999 instead.
Callers should quote reference number 12170082897.