The District Courts deal with criminal matters involving young people who are 17 years old and over. You can find your local district court webpage from
http://www.courtsofnz.govt.nz/district/district. You can be brought before a District Court if you have been arrested by the Police or a Traffic Officer or if you have received a summons (for example, for a driving offence or shoplifting, drinking under age or smoking cannabis).
Appeals, Jury Trials or transfers to High Court
You can get legal aid for these too, and sometimes the same lawyer who acted in the District Court will be assigned; but this is dependant upon the lawyer being qualified in that particular area of law.