If you have made a complaint to Immigration New Zealand and you are not satisfied with their response, you may be able to complain to the Office of the Ombudsman. If the Ombudsman agree, they may choose to investigate your complaint and make recommendations to Immigration New Zealand.
You must have already made a complaint to Immigration New Zealand regarding the issue you want to complain about
You must make your complaint in a timely manner, normally within 6 months of the issue arising
There must be valid grounds for the complaint. Simply disagreeing with a decision rendered by Immigration New Zealand is not normally sufficient by itself to justify a complaint.
Your complaint must not be frivolous or vexatious