Have a look at this page on the IRD website
Exemption from Resident Witholding Tax (RWT) is automatic for Registered NZ Charities provided that the box indicating that KOHA will be an anticipated source of income has been ticked during the application process. Qualifying charities will then be zero-rated for RWT and will be included as a “donee” organisation which will qualify give tax receipts eligible for tax credits when a donation is made.
Consult the above website for information about tax exemptions which may be applicable for other organisations.