"Having now completed a review of this case Crown Law has today filed an application in the High Court to appeal the matter.
"As this case is now before the Court we will make no further comment on the matter."
Judge Cunningham said in the Auckland District Court on July 3 that she was "driven to the conclusion" that Paki would lose out on being a successor if convicted.
"There's only two sons and in my view it's important that the king at the appropriate time has the widest possible choice of a successor and it's important for Mr Paki, as one of those two sons, to have the potential to be a successor in time."
While his drink driving was moderately serious, she said, the direct and indirect consequences of a conviction were "out of all proportion" to the offence.
However, she said she was concerned that alcohol had been a factor in both incidents, and made the ruling conditional on receiving a report from a medical professional clearing Paki of any alcohol addiction or alcohol abuse issues.
He was also disqualified from holding a driver's licence for eight months.
Paki's friends - Te Ahorangi Totorewa, 20, Hamuera Wipoha Pugh, 19, and Raa Ngaru Smith, 18 - were all discharged without conviction in Gisborne District Court over the March burglary and theft incident.
The four had stolen surfboards from a Top Ten Holiday Park and clothes from a man's car after a drinking session in March.
Judge Cunningham also praised the work Paki and his friends had undertaken in terms of restorative justice and community work, as well as an on-going mentoring programme.
Defence for Paki, Paul Wicks QC, said the consequences of a conviction would outweigh the seriousness of the crime, because it would render the teen - who will become a father in September - ineligible for the role of king.
However, police prosecutor F. Gul Qaisrani, opposed a discharge without conviction, saying it would send the wrong message to society.
