Ashley Paul Kelly, 32, appeared in court on Monday visibly unwell.

He refused to speak with a Legal Aid duty solicitor in the cells before his appearance and had rested his head on the bar table once in court, occasionally making unintelligible outbursts.

Magistrate Robert Cook charged Mr Kelly with culpable driving before sending him to hospital under guard for a mental health assessment.

A police statement of facts tendered to court suggested Mr Kelly deliberately steered his car towards the two victims, who were cycling and walking on Alexandrina Drive early on Sunday morning.

The cyclist told police he had heard a car's engine rev before it struck him in the side. The car had then braked, throwing him to the ground.

The driver got out and said something like, "you got what you f---ing deserved, you shouldn't have been on the road you f---ing idiot."

The station wagon drove off and the cyclist took a photo of it before calling police, who arrived to the scene before 7am.

Paramedics took the cyclist to hospital where he was diagnosed with a fractured spine.

Police were at the scene of the cyclist's accident when a purple station wagon approached on Alexandrina Drive. A second cyclist yelled out to officers that the car had tried to hit him.

Police indicated for the car, which had extensive damage to the front windscreen and side, to pull over, which it did. When police asked the driver to turn the engine off, he put it into gear and sped away.

The second cyclist returned and said the car had hit someone.

Police found a man about a kilometre away lying on the cycle path with blood coming from his mouth, his arms and legs tucked into his body and one of his shoes about five metres away.

"Visible tyre marks ran through the grass and dirt to the location where [he] was lying," the statement of facts said. "It appeared the vehicle had travelled off the roadway and directly at [him]."

The pedestrian was taken to hospital where he was diagnosed with a severely fractured jaw, bleeding on the brain, and a fractured tibia.

Police tracked the purple Daihatsu Pyzar to Mr Kelly's Ainslie address, where they found the car. He was subsequently arrested.

In a police interview that afternoon, he told officers another Ashley Paul Kelly with the same birthday was the Daihatsu's owner.

He denied driving the car that morning.

Mr Kelly also said he had only tried to knock the cyclist off his bike and was not trying to hurt him. He said he'd stopped to check on the cyclist, and asked if he'd "seen the light".

He said he'd hit the pedestrian because he believed "G" was trying to knock "Lucille", a friend of 13 years.

Mr Kelly told police he believed the pedestrian was the devil, and his intention on the footpath had been the black line - death.

He faces court charged with two counts of culpable driving causing grievous bodily harm and one of failing to stop for police.

He did not enter pleas.

He will return to court on a later date following assessment.