It is alleged that between 2012 and early 2015, Hunia made false entries in the agency's accounting system.
There were also allegations she misused her employer's company petrol and travel cards, including for international flights.
According to court documents, by November 2013, Hunia racked up a $9846 bill on a fuel card and a year earlier caused a loss of more than $20,000 to PT&I.
The details of how that money was allegedly obtained were not specified in charge sheets.
The head of PT&I, trade commissioner Michael Greenslade, previously told the New Zealand Herald that "stakeholders were advised of the situation" as the investigation into Hunia progressed.
He said the situation was frustrating because it mostly pre-dated his tenure, which began in November.
Hunia will appear in court again next month.