Officers say anyone who sees Daniel Brown, 22, should not approach him, but ring 999.
Brown ran off from officers shortly before 9am on Wednesday as he was being escorted to a police van outside the hospital, where he had been for treatment.
He fled towards the Shakespeares tower blocks pursued by officers but managed to get away.
Despite extensive inquiries he has not been found.
Brown was arrested on Tuesday after being circulated for recall to prison following his release in March from an 18-month sentence for possessing an imitation firearm with intent to cause fear of violence.
Detective Inspector Phil Jackson, of Leeds District CID, said: "While we are satisfied that Brown presents no immediate danger to the public, we urgently need to find him and take him back into custody.
"We have been carrying out extensive enquiries and visiting a large number of addresses linked to him and that work is ongoing. We are now asking for the public's help in tracing him as we believe he will still be in Leeds area.
"He is known to frequent the city centre and we would like to hear from anyone who has seen him or who has any information that could assist the investigation. We would advise anyone who sees him not to approach him but to contact police immediately on 999.
"We would also like to hear from anyone who saw him in the area surrounding the hospital at the time of his escape on Wednesday morning. He will have needed somewhere to hide or transport out of the area and was wearing two pairs of handcuffs which are likely to have required cutting equipment to remove.
"I would like to remind people that it is a criminal offence to assist someone who is unlawfully at large and we will take robust action against anyone who we establish has been helping Brown."
Call 101 or Crimestoppers anonymously on 0800 555 111.