Manuel and Hamiora-Smith used a utensil to jemmy a lock and scaled a fence to escape the facility two days ago.
The public were warned not to approach the pair, who were believed to have hitch-hiked out of the city on Monday night.
Senior Sergeant Andrew O'Reilly of the Waikato District Command Centre said advice from medical staff suggested neither man posed a specific risk to the public, but both had a history of violence and police advised the public not to approach them.
The pair were reported absent without leave from the Selwyn St centre around 9.20pm on Monday, Mr O'Reilly said.
"Both men were being treated as in-patients under mental health legislation before they absconded," he said.
Meanwhile, the father of a man who was found dead in the Waikato River after leaving a mental health facility has asked why it had taken the escape of two men with a history of violence for the facility to launch and independent review.
Nicholas (Nicky) Taiaroa Stevens was found dead in the river on March 12. He had been missing for three days after leaving the Henry Rongomau Bennett Centre at Waikato Hospital.
Dave Macpherson, father of Mr Stevens, told TV3 he had "pleaded" with the staff at the centre against letting his son out for fears he would harm himself.
"We complained well in advance of him disappearing about the management processes and security processes that led to him getting out."
Mr Macpherson said following his son's death, the facility began an internal inquiry, but he asked for an independent review.
Waikato District Heath Board chief executive Nigel Murray told TV3 that an independent review would be carried out following the escape of Manuel and Hamiora-Smith.
Mr Macpherson said his family was "very hurt" that it took a second incident for the review to come.
"It means our son's death doesn't count for anything in that sense.
"Where was the answer to us, the response to us when we requested a proper review and an independent review?"
Dr Murray told TV3 that the two scenarios were "quite different circumstances".
He said he had expressed his "deepest condolences" publicly to the family of Mr Stevens, but would not be speaking to the family until after the review.
Dr Murray thanked the police for their work in apprehending the two patients.
"We are looking forward to getting them back so that we can continue their rehabilitative care," he said.
"In the interim, I am thinking very carefully about the terms of reference for the external review I signalled I would undertake on our mental health services."
The independent review would look at clinical practices, systems and processes and if there were any physical issues with the centre itself.
It would also consider any similarities between recent incidents in which patients have left the centre.
"With regard to Nicholas Stevens' tragic death, I again extend my deepest condolences to his family. I want to be totally transparent. I will be meeting with Nicholas' family when I have the information I need. The meeting will occur as soon as practicable.
"I can confirm we have included in the review of Nicholas' death an independent psychiatrist and mental health nursing leader.
"The review will be conducted under standard Health and Quality Safety Commission guidelines. The matter has also been referred to the coroner."