But the higher court will first investigate whether Ashley Paul Kelly is fit to plead to the charges - including attempted murder - stemming from the early morning incident.

Mr Kelly, 33, was arrested on June 4 after he allegedly struck a cyclist and a pedestrian on Alexandrina Drive in Yarralumla.

Documents tendered in court on an earlier occasion allege Mr Kelly first struck the cyclist, who was knocked to the ground.

The cyclist took a photo of a purple station wagon before calling police, who arrived on the scene before 7am.

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

Police were at the scene of the cyclist's accident when a purple station wagon approached on Alexandrina Drive.

Officers indicated for the car to pull over, which it did. But when police asked the driver to turn the engine off, he allegedly put the car into gear and drove off.

A cyclist rode up to police and said a purple car had hit someone further along the road.

Police said they 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 documents suggest.

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

Police said they tracked the purple Daihatsu Pyzar to Mr Kelly's Ainslie address. He was arrested.

In court the following day, Mr Kelly was referred for a mental health assessment.

On Thursday, Magistrate Karen Fryar committed the man to stand trial in the ACT Supreme Court on one charge of attempted murder, two of culpable driving causing grievous bodily harm and one of intentionally inflicting grievous bodily harm.

A charge of failing to stop for police was also transferred to the higher court.

The magistrate, who had already found there was a "real and substantial" question about Mr Kelly's fitness to plead, reserved the question for investigation by the higher court.

She ordered a psychiatrist see Mr Kelly to assess him.

Canberra law says a person is unfit to plead if their "mental processes are disordered or impaired" to the extent that, among other matters, they cannot understand the nature of the charge or the substantial effect of any evidence that may be given in support of the prosecution.

At an appearance in court in July, Mr Kelly's lawyer entered pleas of not guilty to charges of culpable driving causing grievous bodily harm and failing to stop.

The court heard he would fight the charges on mental illness grounds.

No pleas have been entered on the remaining charges.

Mr Kelly remains in custody.

The case is due in the higher court on October 26.