The incident occurred at the rear of the Wetherspoons Royal Baths pub on Parliament Street at about 7.30pm on Saturday 1 November 2014.
A local man aged in his early 50s suffered a serious head injury after allegedly being punched to the ground.
Paramedics treated him at the scene before he was taken by ambulance to Harrogate District Hospital where his condition is described as “critical”.
A 43-year-old man from the York area also required treatment for facial injuries after being assaulted at the same location. He is assisting the investigation.
Extensive police enquiries remain ongoing to establish the full circumstances surrounding the incident and to locate the man suspected of the assaults.
The suspect is white, aged in his mid-40s, medium build, with a bald head and short hair around the sides. He was wearing a dark-grey, long-sleeved jumper.
Customers inside the busy pub had to leave the premises at about 8.30pm while detectives and crime scene investigators carried out examinations.
Witnesses or anyone with information that could assist the investigation or help locate the suspect, are urged to contact North Yorkshire Police on 101, select option 2, and ask for Harrogate CID.
If you prefer to remain anonymous, please call Crimestoppers on 0800 555 111 quoting reference number 12140189150.