The investigation was also hindered by the dangerous state of the building, with holes in the floor on the ground level and the floorboards burned through on the upper floor.
However, the occupant reportedly told people at the scene a child may have been playing with a lighter inside.
Beer had been unable to verify that, but could not discount it either.
The child had been referred to a children’s fire awareness education programme.
Beer urged all parents and caregivers to ensure that matches and cigarette lighters were kept well out of reach of children.
The building is owned by Kāinga Ora (formerly Housing New Zealand).
Te Tai Tokerau regional director Jeff Murray said Kāinga Ora was carrying out a damage assessment and securing the duplex properties.
“We are currently working with the customers of both properties to find them alternative accommodation,” he said.