The man pictured left Leeds General Infirmary at about 5.37pm yesterday (Sunday) despite needing medical attention.
He was taken by ambulance to hospital after he was found collapsed on the street at the junction of Torre Lane and York Road at about 4pm that day.
The man was not able to provide a name or details to hospital or ambulance staff and later walked away from the hospital.
He is described as being in his 50s or 60s, 5ft 9in, and unshaven with dark grey hair. He may be called Greg.
Detective Inspector James Entwistle, of Leeds District CID, said: "We are very concerned for the well being of this man who is suffered a potentially life threatening head injury and needs immediate medical attention.
"We are appealing to anyone who knows him, saw him leaving hospital or may have seen the original incident at the junction of York Road and Torre Lane in which he was injured, to contact us as a matter of urgency.
"I would ask anyone who can assist to call the Special Operations Room at Leeds District HQ through 101, referencing police log 1171 of January 8."