You can apply for a death certificate through Births, Deaths, and Marriages.
Under New Zealand law, you must let Births, Deaths, and Marriages know of any deaths in New Zealand within 3 working days of that person’s burial or cremation. The person in charge of the funeral arrangements, like a funeral director, needs to collect all the information needed and send this to Births, Deaths, and Marriages for registration. You can find information on what to do on the Department of Internal Affair’s website.
Once registered, Births, Deaths, and Marriages will issue a death certificate — there may be a fee you’ll need to pay.