Police prosecutor Heath Karlson asked the court to order the defendant to meet with a forensic nurse who could assess his mental health.
Karlson said the man was a potential suicide risk.
But defence counsel Rob Weir, who is yet to meet his client, asked for that to be delayed so he could make his own inquiries.
The mental health assessment order was not made.
Karlson then sought a no-contact order in favour of the man's children, which was granted by the court.
The accused's appearance was initially before Judge Gregory Hikaka but near the end of the hearing Judge Tony Greig was called from another courtroom to take over.
Judge Hikaka had also appeared via AVL as he is currently taking part in a district court trial which has seen a number of judges preside over courts remotely.
But when the connection with Judge Hikaka was lost during the hearing and the court was unable to reconnect him, Judge Greig, who had spent the day presiding over a trial, was asked to take over in person.
The man was remanded back into custody to appear in the High Court on March 8.
On Monday, police were called to the woman's Carrington St address around 2pm, followed by an ambulance.
The man was taken into custody at the scene and the house was cordoned off shortly after.
Later in the day, a murder charge was filed against him.
It is understood the woman was known to the man and no one else is being sought by police in connection to her death.
Police, as well as a team of forensic experts, were at the house for much of today conducting an investigation.
