Ceol and Muir, which is owned by Italy-based Rafael Grozovsky and his Argentina-based brother Federico Grozovsky, was granted consent in February 2014 to purchase the 1317-hectare Onetai Station in Awakino, Taranaki for $6 million.
The Overseas Investment Office (OIO) reviewed its files after the scandal broke.
"While the OIO was conducting a search of its records, the OIO noted that Ceol & Muir's registered office is at the Panama office of Mossack Fonseca," the agency said.
"The OIO has no evidence that would suggest that this connection with Mossack Fonseca is in breach of any laws."
However, Ceol & Muir had failed to meet some of the conditions of its OIO consent, which included "good character" requirements.
It had to report to the OIO on these conditions every year, and most recently reported back in February.
The OIO said it was "not content with progress made" on fulfilling these conditions, in particular a requirement relating to the improvement of the property.
Earlier today, Labour MP David Cunliffe identified Ceol and Muir as the business whose investment in New Zealand was being investigated by the OIO.
Mr Cunliffe said Land Information Minister Louise Upston should now investigate and disclose how many companies had links to Mossack Fonseca.
A spokesman for Ms Upston said an initial review by the OIO of its records had not picked up any further cases with connections to the Panama law firm.
It was now undertaking a more comprehensive review of all of its decisions.
Mr Cunliffe said: "The Government's contention that only one application is caught up with Mossack Fonseca needs further scrutiny, especially when the OIO admits it has taken a 'lighter touch' in rejecting applications.
"The OIO should be our safeguard, but with only one application declined since 2011, questions should be asked about the effectiveness of its oversight."