When he escaped again, on August 20, hospital security officers and police searched. But it was not until nearly six weeks later, on September 30, that his body was found in dense bush near the hospital campus.
"We can't comment because it is before the coroner," said the DHB's communications manager Lauren Young, adding, "Our sympathies are with the family."
As well as the coroner's investigation, an internal investigation is being done by the DHB.
A police statement in September seeking public help to find Jonas said he may have been sleeping on the streets of central Auckland. "Due to his health he may be unpredictable and members of the public should not approach him," the police said.
The relative said Jonas' family were upset that he had been able to escape after he was admitted to hospital to help with his problems.
The Labour Party has cited Jonas' case in support of its demand for the Government to hold a national inquiry into mental health services.
Labour's acting health spokesman, David Clark, said DHBs were getting insufficient funding to meet the rising demand for acute mental health care.
He produced figures supplied by Counties Manukau indicating Tiaho Mai is overcrowded. Its average occupancy has hovered between 95 and 99 per cent this year.
The target is 85 per cent.
On average at least one staff member a week works 60 to 80 hours.
Health Minister Jonathan Coleman has refused to hold an inquiry.
"A national inquiry in itself isn't going to improve access to services."
He said the Government continued to improve mental health services through a wide range of initiatives and frameworks.
"Demand for mental health services has increased from 2.3 per cent of the population a decade ago, to 3.5 per cent of the population in the last year - from around 96,000 people, up to 164,000.
"We've increased mental health and addiction services funding from $1.1 billion in 2008/09 to over $1.4b for 2015/16," Coleman said.
The DHB's chief medical officer, Dr Gloria Johnson, would not answer questions about Rika, but said that while non-forensic mental health units must minimise the risk of patients harming themselves or others, they were not prisons. "We are preparing people for the community.
"It's not appropriate that they are so secure that people can't leave.
"We need to help people accustom themselves for taking responsibility for what they are doing and where they are," Johnson said. "That means a risk that people will leave if they really want to."
But Dave Macpherson, whose 21-year-old son Nicky Stevens was found dead in the Waikato River last year after he was released from a Waikato DHB mental health unit, said Johnson's comments indicated widespread problems in properly assessing the risks of patients harming themselves or others.
"Do you want someone to die because you don't want it to feel like a prison? They're chucking the baby out with the bathwater by saying something like that," said Macpherson, who has been elected to the Waikato DHB and will campaign for proper risk assessment following his own son's death, and now the killings by Ross Bremner.
Bremner's body was found alongside those of elderly couple Mona Tuwhangai and Maurice O'Donnell, four days after he stabbed his mother, Clare, 60, to death and critically injured his father, Keith, 64, at their Otorohanga home.
The Government is under increasing pressure to hold an inquiry after deaths and localised inquiries at several DHBs' psychiatric services found serious flaws.
The Public Service Association last month expressed its concern at the "serious" staffing issues at state-run psychiatric hospitals in Auckland. This was after the Waitemata DHB had closed eight of the 35 beds at the He Puna Waiora mental health unit at North Shore Hospital in Takapuna, because of staff shortages.
Staff told the Herald last month that they had begun to fear for their lives at work. They were working double shifts and extended shifts, and "burning out", they said.
Many had left because of safety fears and the shortages had led to an increase in assaults by acutely unwell patients on staff and other patients.
Where to get help
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Depression helpline: 0800 111 757 (available 24/7)
• If it is an emergency and you feel you or someone else is at risk, call 111.