A NSW officer tasked with bringing a mentally ill man back to hospital chased and shot him, despite warnings he was frightened of police.

Elijah Holcombe died after being struck by a single bullet in the chest fired by plain-clothed officer Senior Constable Andrew Rich in Armidale, in northern NSW, on June 2 last year.

On the opening day of a two-week inquest into Holcombe's death, Armidale Coroner's Court yesterday heard police were warned the Macquarie University psychology student suffered from a mental illness characterised by paranoid episodes and a phobia of police.

Counsel assisting the coroner, Chris Hoy, said an "integral component" of the inquest would be to determine whether Holcombe's death was a result of justifiable homicide.

The inquest, which will hear from 71 witnesses, will also look at the role of police officers and how they interact with people with a mental illness.

In the months leading up to his death, Holcombe, who had battled depression for eight years, was living with his parents, Jeremy and Tracey, in Wee Waa, in the state's north, because of concerns about his mental health.

Four days before his death, Holcombe was treated at nearby Narrabri Hospital for "superficial self-mutilation cuts" to his wrists. He was prescribed the anti-depressant Zoloft and the anti-psychotic Risperidone and released the same day.

On June 1, Holcombe took his father's car and drove to Armidale. Mr Holcombe reported the matter to Narrabri police and warned them his son was experiencing paranoid delusions but "would not hurt anybody".

When Holcombe arrived at Armidale, he went to the police station, admitted stealing the car and asked to be taken to Armidale Hospital where he was assessed by nurse Carla Rutherford.

In a witness statement, Ms Rutherford said Holcombe appeared paranoid and despite attempts to keep him at the hospital as a voluntary patient, he was legally allowed to walk out.

When senior constables Rich and Christopher Dufty learned Holcombe had discharged himself, they went to the hospital and nurse Robyn O'Brien asked them to bring him back because of concerns about his mental health.

Soon after, the officers spotted Holcombe walking along Rusden Street, in Armidale's city centre. There was a brief exchange before Holcombe fled, pursued on foot by Senior Constable Rich.

Holcombe ran into a coffee shop, grabbed a bread knife and then fled out the back door to Cinders Lane. Senior Constable Rich confronted Holcombe in the laneway and asked him three times to drop the bread knife before shooting him in the chest.

The inquest heard from Narrabri officers Senior Constable Brett Allison and Leading Senior Constable Alexander Coates who both said they had not received formal training in how to deal with mentally ill people.