New Zealand Law
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If you have been convicted, then your next step would be to appeal the conviction. I am surprised you were convicted if the judge commented that she was lying, and enquire whether there was other evidence which supported the police prosecution case. You have not said if you had a lawyer to represent you for the case, but if you appeal would need one
If you take the case on appeal you should be aware that the judge in the High Court is limited in what they can do. You need to point out a mistake of law made by the district court judge, because judges on appeal do not like to overturn decisions on the facts. This is because the appeal is run on the transcript of the evidence, and the witnesses are not called again for the High Court. This means that the district court judge has the advantage of assessing credibility of the witnesses, but the High Court does not have this. So the judges are reluctant to overturn findings on credibility.