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The work by the colonial-era portraitist went missing between December 27 and January 3, and police are appealing for information.
Sleep 'tis a Gentle Thing was taken along with other unique artworks and antiques.
The painting itself has not been recovered, police said.
This afternoon, a 45-year-old man pleaded not guilty at Hamilton District Court to the charge of burglary and was released on bail to reappear in March.
A 49-year-old man was remanded in custody with no plea and will reappear in February.
Both men have interim name suppression. A third man is expected to appear in court later today.
Police said they searched a Hamilton address on Saturday and recovered a quantity of stolen property.
Goldie produced several versions of the Hori Pokai painting.
The director of the International Art Centre, Richard Thomson, sold one for $454,000 in 2009.
After reviewing a police photo of the item, he said it looked like the same one and it could be worth $1 million now.