Being taken to an emergency department or police cells would be kept as a last resort.
In 2016 police received 46,359 calls for mental health issues, about 90 calls every 24 hours.
Internal police data shows demand for mental health responses has increased by around 9 per cent each year for the past 10 years, and is forecast to continue.
"The Independent Police Conduct Authority is concerned that police are increasingly acting as first responders to people who should more appropriately receive a mental health response," police wrote in a document for proposal funding.
"As a result mentally impaired people are not always dealt with by police in a manner that is conducive to their mental and physical wellbeing, increasing their distress and placing them at greater risk of harm while in police custody."
It said that responding faster and more effectively could stop people with mental health issues, as well as their family members, from escalating into the justice system.
Assessing people in their own home would also allow the team to see other factors in a person's mental distress, such as housing, employment, income support, or alcohol and drug abuse.
The co-response trial will pilot three teams, two of them city locations and one rural, able to respond between the peak hours of 3pm to 1am.
In documents pitching the change to the Government, police admitted it was needed because of stretched resources.
"The co-response service is a mechanism for improving the response mentally unwell people receive, as the Ministry of Health has indicated it has a limited capacity to respond to increasing demand.
"This 'high needs' population group is not currently receiving a targeted, holistic, or timely response to their needs.
"This means their level of care may be unco-ordinated and is not provided by the most appropriate services."
The internal documents show police were reluctantly being called on as the first response for people suffering a mental health episode.
"As police response is timely and 24/7 they are often called upon to provide both first response and management of not just offenders with mental illness who end up in the criminal justice system, but in many instances police are responding to incidents where no crime has been committed.
"The lack of capacity in the Health Crisis Response Services results in delays to resolve mental health events and unnecessary detentions of people in custody."
The police hope the model will be so successful, it will pay for itself.
They calculate that each incident the co-response team attends will save $310 from transferring the patient to emergency departments, as well as saving two hours of police wait time.
They estimate a 75 per cent drop in mentally ill people being held in police cells for an acute mental health assessment, with the majority of people being able to receive care from the co-response team in their home.
This was backed by comparison to a similar system in Australia, which showed that between 73 percent and 78 percent of patients were assessed at the scene and able to stay where they were.
The Australian model also showed a quicker response time, slashed from from two hours and 46 minutes under previous emergency response, down to just 52 minutes in a co-response model.
"Providing a co-ordinated and comprehensive service from the outset means people are more likely to receive the care they require when they need it, reducing repeat demand, and resulting in fewer emergency service calls to police and ambulance," proposal documents said.
If successful, police hope the trial could become a mainstream service.
The locations and official start date of the trial is still being negotiated with DHBs around the country.
Police declined a request for interview while those negotiations were still ongoing.
• Lifeline: 0800 543 354 (available 24/7)
• Suicide Crisis Helpline: 0508 828 865 (0508 TAUTOKO) (available 24/7)
• Youthline: 0800 376 633
• Need to talk? Free call or text 1737 (available 24/7)
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• Whatsup: 0800 942 8787 (1pm to 11pm)
• Depression helpline: 0800 111 757 (available 24/7)
• Rainbow Youth: (09) 376 4155
• Samaritans 0800 726 666
• Rural Support Trust: 0800 787 254.
• If it is an emergency and you feel like you or someone else is at risk, call 111.