The German law on citizenship mandates that German citizens who voluntarily apply for and accept New Zealand citizenship will automatically lose the German citizenship if they have not been granted a permission to retain the German citizenship prior to becoming New Zealand citizen. This “Beibehaltungsgenehmigung” is granted by the competent authority in Germany on an individual basis. To obtain the permission, you must prove that you still have substantial ties to Germany and are in a personal situation in which the obtainment of the dual citizenship would be beneficial to you and/or avoid individual detriments. Please note that applications have to be submitted to the German Embassy in Wellington and that proficiency in German is mandatory.
More information on the “Beibehaltungsgenehmigung” (in German only) here.