The Dunedin health professional accused of murdering a 16-year-old girl is set to apply to be released on bail.

The 30-year-old defendant, who allegedly killed teenager Amber-Rose Rush on February 2, will apply for electronically monitored bail at a hearing on April 9.

The date for the bail application was set at a short hearing in the High Court at Dunedin yesterday, where the defendant was represented by defence counsel Marie Taylor-Cyphers and Justice Gerald Nation appeared by audiovisual link.

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At the defendant's last appearance before the High Court at Dunedin on March 6, he pleaded not guilty to murder and four charges of threatening to kill.

His denials were so vehement, he had to be told by the registrar to wait until the charges were read before he entered the pleas.

At that appearance, Justice Nation declined an application to continue name suppression, but this decision was appealed.

The Court of Appeal will now set a date for the issue to be argued.

Under such circumstances, suppression must continue, in case the appeal is successful.

Amber-Rose was found dead by family members at her Corstorphine home the day after her alleged murder.

Police said her alleged attacker was known to her and they were not seeking anyone else.

In the days following Amber-Rose's death, police searched waterways at Blackhead and confirmed they found ''an item of interest'', understood to be a cellphone.