The Mount Aurum homestead and an outbuilding at the remote Department of Conservation campsite near Queenstown were destroyed in the fire.
A local woman and a man of unknown abode contacted police the following day to admit they spent part of the night in the building, and lit a fire in a bedroom fireplace before later putting it out with water.
A fire investigator's report, released to the media on Monday, found the fire's cause to be ''undetermined''.
But it also found the fireplace's grate was ''remarkably clean'' when examined afterwards, with no sign of a fire having being lit inside it.
Otago-Lakes CIB head Detective Senior Sergeant Malcolm Inglis told the Otago Daily Times police had to prove the pair either intentionally set the building on fire, or were ''grossly negligent''.
''We don't feel like it was a wilfully, purposefully set fire, and it didn't reach the standard of gross negligence.
''Obviously they didn't see the sign saying 'no fires'.''
The matter had been passed to the Department of Conservation to see if there was ''any other form of resolution''.
Doc Wakatipu operations manager Geoff Owen said the department would consider its options under the Reserves Act 1977 and the Heritage New Zealand Pouhere Taonga Act 2014.
Arrowtown resident Colin Macnicol is a nephew of Mona and Archie Macnicol, who lived in the homestead from 1940 to 1956 as runholders of the former Mount Aurum Station.
Mr Macnicol said he and his extended family were ''shocked and disappointed'' no action was being taken.
''It's an open invitation for anybody who wants to have some fun while under the influence of something to go and burn down a Doc building somewhere, knowing there'll be no penalty.
''Imagine the furore there would be if somebody burned down the Stone Store at Kerikeri or the Treaty House at Waitangi?
''The Mount Aurum homestead and school are just as valuable to the people of this area.''
Witnesses to the fire say the couple arrived after 6pm on New Year's Eve and started to ''party'' on the homestead's veranda.
About 10pm a camper saw a ''red glow'' in the bedroom that he thought came from a fire.
When campers noticed flames coming from the building just after 2am, the couple had gone.
Queenstown residents Lee Gamble and Morgan Harteveld were among a group of six friends who joined forces with two other campers to fight the fire.
Mr Gamble said they were still angry the couple had put them all in danger by leaving the campsite without waking them.
If the couple - particularly the ''local girl'' - had owned up to their mistake and apologised, he and his friends would have accepted it and moved on.
Mr Harteveld said he was disappointed no charges had been laid, and questioned how it was ''possible to walk away clean from such a crime''.
''They could've killed us.''
