A Perth man detained indefinitely for killing his three-year-old son will return to an Adelaide court in May to determine whether he will be allowed overnight release.

Aliya Zilic was found not guilty because of mental incompetence of the murder of his son Imran Zilic in April 2008, and has been held under mental health supervision at James Nash House.

Trish Johnson, for Zilic, told the South Australian Supreme Court on Thursday her client should be allowed to stay overnight at nearby Ashton House - a 10-bed lower-security mental health unit.

She said Zilic would be secure at the Adelaide facility because an alarm around the perimeter activates at night.

"During the day, if he walks off the premises he could potentially be gone for half an hour or an hour without staff members being aware," she said.

"If he were to walk off the premises or attempt to abscond (at night), staff would be alerted much more quickly."

Camera Icon Imran Zilic, 3, was killed by his father, Aliya Zilic, close to a decade ago. Credit: Supplied

But prosecutor Lucy Boord urged Justice Greg Parker to grant only stage one of Zilic's application, which involves walking alone and visiting Ashton House during the day.

"Moving from being at Ashton House for some short periods during the day to overnight leave is a significant reduction in his level of supervision," she said.

She said Justice Parker should order a report on how Zilic had handled stage one before he allowed stage two overnight release.

Justice Parker agreed, and granted the first stage of the application, ordering the case return to court in May for an update on Zilic's progress.

Zilic was detained in 2010 after a Supreme Court justice ruled that he was suffering mental impairment at the time he cut his son's throat.

The court was told he had taken the boy from Perth and had embarked on a "bizarre odyssey" through Australia's outback, before killing him and dumping his body in Coober Pedy.

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