The camera did not appear to be directed towards the spot previously occupied by the most valuable of the medal sets - the Victoria Cross and Bar awarded to Captain Charles Upham, which experts say are worth more than $3 million.
Defence Force headquarters in Wellington says the police have told it not to comment on security at the museum.
Inquiry head Detective Senior Sergeant Chris Bensemann said officers were baffled why the thieves removed the panes completely from one cabinet, but then took none of the four medal sets in the case - including two VCs.
He would not confirm a TV3 news report that the thieves used a "Plan B" to get into the museum, after first trying to drill through a different door to the fire escape which they used to enter.
As police continued their scene examination at the museum yesterday, the cafe was open but the displays remained closed and areas outside the building were still cordoned off.
Closed-circuit television footage from the museum stretching back several weeks will be examined in the search for clues to the thieves.
Untouched medals
* Thomas Cooke, VC
* Percy Valentine Storkey, VC
* Bernard Diamond, VC
* William James Hardham, VC
* Samuel Austin, NZC
* Henry William Northcroft, NZC