The pair charged in relation to the death of Constable Matthew Hunt have kept their names secret - for now.
Constable Hunt was shot, and another officer injured, during a routine traffic stop in West Auckland on 19 June.
A 24-year-old man is now before the court charged with murder, attempted murder and dangerous driving causing injury.
A 30-year-old woman has also been charged with being an accessory to murder.
The woman was refused interim name suppression when she first appeared in the Waitakere District Court last month.
However, she kept her name secret in light of an appeal to the High Court that was unsuccessfully argued before Justice Venning this morning.
The judge declined the appeal but granted interim name suppression until 4pm today so her lawyer could take instructions on a possible further appeal.
The male defendant's application for name suppression was granted a brief adjournment this morning and will be heard on 31 July.
Both defendants pleaded not guilty to the charges last week and are due to go to trial in July 2021.