The police said various stolen pieces of property, including the carved monument were found. Kaiapoi Pā is an important site in local and tribal history and the monument dates back to the late 1800s.
White-Parsons appeared in court on June 2 and was remanded in custody for a further appearance by video-link, on charges of burglary and receiving stolen property.
When he appeared again, he was also charged with receiving a large water tank valued at $3000 from unknown persons.
Christchurch District Court Judge Tony Couch told defence counsel Nadine Girgis that White-Parsons needed to enter pleas to the original three charges, so she announced he would plead not guilty and elect trial by judge-alone. He was remanded without plea on the latest charge.
But Judge Couch also told the police that the charge relating to the carving referred to it having "an unknown value" - and that is not allowed under the justice system.
Charges have to have a value on items, but at their most vague, they must refer to an item being either under or over $1000 because that changes the charge and the penalty that can be imposed.
Prosecutor Sergeant Kathy Pomfrett said police regarded the carving - which has cultural significance - as being "priceless".
However, she said they were seeking an opinion about what its value could be, and would seek to add the figure to the charge at the next appearance.
White-Parsons is due to appear for an application for release on electronically monitored bail on June 29, and a Crown case review on the other charges on July 26. He remains in custody in the meantime.