But they said any connection between the break-ins and damage and possible heritage activists would be part of the investigation.
Last week the Malcolm Walker-designed property on Hakanoa St in Grey Lynn " which is owned by Justine Muxlow and Daniel Birt "was burgled and fires started in a number of rooms.
Fire gutted a room next to a child's bedroom, and a window exploded.
The pair and their two young children were not home.
Last October, electrical equipment was stolen and taps were turned on, flooding the family home.
Last May the house, built in 2012, featured on TV One show Art of the Architect. The show covered the granting of resource consent for a modern build on a street lined with villas and bungalows.
Muxlow and Birt said their brick-clad bungalow had no insulation, was rotting and covered in black mould.
They said it would cost more to renovate than rebuild.
The bungalow was relocated to a site in Kingsland and was replaced with the house designed by well-respected architect and cartoonist Malcolm Walker. On Art of the Architect, Birt had concerns about opposition to the build. "I just hope no one breaks in there and spray paints all of my walls, because that could happen," he said.
Neighbours told the Herald on Sunday they would be disappointed if the attacks were related to the modern build.
"It is absolutely terrible and we just want whoever did this to be caught," one neighbour said.
"They are a lovely couple and have young children. They need to feel safe."
Other neighbours tried to put out the fire and called emergency services.
Anyone with information about the burglary or the arson is asked to contact Avondale CIB on (09) 820 5776.