From 2009 to 2011, 60 per cent of claims came from these households compared with 13 per cent with an audible alarm and 16 per cent from homes that were not monitored.
AA Insurance operations chief Martin Fox said simple deterrents could reduce risk, especially given that thieves would use any means to gain entry.
One customer reported that her house was broken into by thieves who used the rubbish bin to climb through the window.
"Securing your home both at night when you are asleep, and during the day when you are out, should be common sense for all New Zealanders. Our claims data clearly shows that having a house alarm installed and warning stickers on display deters thieves.
"Simple things like leaving a recycling bin outside your home or letting your mail pile up while on holiday can be an advertisement that your property is unoccupied.
"Asking a trusted neighbour to look after your mail and recycling can reduce signals that you're not at home," Mr Fox said.
After 1998-99, when 50,464 offences were recorded nationally, home burglaries fell to 35,966 in 2004-05.
However, for the past three years the number has averaged 42,474.
In Auckland, the old Auckland City area had the most burglaries, with 6507 recorded in the last June year. Counties Manukau was next with 5373, followed by Waitemata with 4420.
Flat hit three times
Louise Hilsz's Auckland flat was targeted by burglars three times in the year - twice during the day.
The 27-year-old and her partner came home to their Epsom flat last March to find the place had been ransacked.
"It's pretty ballsy to rob someone's house at 3 o'clock on a Friday afternoon," Ms Hilsz said.
Thieves got in through a window left open to let air escape from a clothes drier, as the flatmates had thought it was too difficult to access. During the second, a night-time incident in June, thieves had shown how resourceful they could be, she said. "They'd gone underneath the house and found old doors to prop up against the side of the house. They'd come through a second floor window.
"I dread to think if the burglar had woken anyone up, my partner would have killed him."
An alarm hadn't been fitted by the second incident, but is now. Extra latches have been fitted to windows and the flatmates are now super-sure about closing them. Burglars visited again in September. She wishes now the flat had been quicker to get an alarm fitted.