At Counties Manukau, officials are investigating the suspected suicide of mental health patient Jonas Isaac Rika, 21, who had escaped in August from an unlocked ward at Tiaho Mai, an acute mental health unit at the Middlemore Hospital campus.
Greens health spokeswoman Julie Anne Genter said: "The data shows mental health services are under pressure across the country. That is consistent with stories from staff and people seeking to access mental health services."
She repeated the call for a national inquiry into mental health services.
Health Minister Jonathan Coleman says a national inquiry is unnecessary.
Mental illness is an important risk factor for suicide.
The ministry report indicates the age-standardised rate of suicides by people aged 10 to 64 who had had contact with mental health or addiction services in the year before their death has declined by more than a quarter since 2001.
The ministry's director of mental health, Dr John Crawshaw, said progress had been made on suicide prevention, but not enough.
"Suicide rates in New Zealand generally had been decreasing but more recently they've plateaued and that's not good enough.
"This trend is also reflected in the rates for those accessing mental health services. The statistics are still too high and collectively, we all need to do more."
The West Coast DHB's clinical director of mental health services, Dr Cameron Lacey, said it takes adverse events very seriously.
"We place a high importance on identifying any such serious adverse events, and use these to look for ways to prevent such occurrences happening again."
"We are committed to improving all aspects of service quality and it is pleasing to note strong performance in the other 11 quality indicators identified in this report."
The Auckland DHB said that at any one time it has more than 6800 people receiving care from mental health and addiction services provided or funded by the DHB.
"The recovery goal is for people to return to independent, functional living in the community. In the in-patient setting people receive health care to help them develop an increasing level of autonomy and freedom of movement as they recover enough for discharge."
Number of suspected suicides and other serious adverse events by mental health and addiction service patients in 2015 by district health board:
Auckland 35
Bay of Plenty 5
Canterbury 16
Capital & Coast 13
Counties Manukau 6
Hawke's Bay 5
Hutt Valley 5
Lakes 4
MidCentral 11
Nelson Marlborough 2
Northland 8
South Canterbury 3
Southern 23
Tairāwhiti 2
Taranaki 0
Waikato 14
Wairarapa 1
Waitemata 19
West Coast 10
Whanganui 3
Total 185
Where to get help:
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youth services: (06) 3555 906 (Palmerston North and Levin)
• Youthline: 0800 376 633
• Kidsline: 0800 543 754 (available 24/7)
• Whatsup: 0800 942 8787 (1pm to 11pm)
• Depression helpline: 0800 111 757 (available 24/7)
• Samaritans: 0800 726 666 (available 24/7)
If it is an emergency and you feel like you or someone else is at risk, call 111.