But a former ACT prosecutor has told the inquiry into Eastman's murder conviction she believed he was fit to plead.

Eastman was convicted of slaying Australian Federal Police assistant commissioner Colin Winchester in January 1989. The inquiry was ordered by the ACT Supreme Court last year after ''fresh doubt'' about Eastman's guilt emerged.

The inquiry is looking into whether Eastman's mental fitness should have been considered during the 1995 trial.

On Tuesday the inquiry heard for a third time from former ACT prosecutor Jennifer Ann Woodward, who ran the murder case before trial judge Ken Carruthers.

She said the Crown considered offering Eastman a deal of diminished responsibility for a manslaughter charge before the trial.

But Lieutenant-Colonel Woodward, now a judge of the Australian Military Court, thought Eastman was fit to plead. However, she believed the issue should have been raised with the trial judge.

Colonel Woodward said the issue was discussed by the prosecution team but not pursued.

The inquiry also heard from Paul Anthony Jones, an Australian Federal Police officer involved in the murder investigation.

A note prepared by Detective Superintendent Jones in April, 1995, said former ACT Supreme Court deputy registrar Jill Circosta had sought 24-hour access to police on the instruction of Justice Carruthers.

''Ms Circosta will be the middle point of contact in order that police and Justice Carruthers remain free of any allegations of having an improper working relationship,'' the note said. ''Police were advised by Ms Circosta that Justice Carruthers may require periodic bomb searches of his vehicle.''

A note in Superintendent Jones' official police diary on May 22, 1995, then showed the officer contacted the bomb squad to obtain a ''self-help'' video on searching vehicles for explosives to give to Justice Carruthers via Ms Circosta.

Superintendent Jones told the inquiry he could not remember obtaining or passing on the video.