If you are trying to get official information from central or local government and they refuse, you can ask the Ombudsman to investigate. If they rule that you should get the information, then the entity must give it to you, unless they veto it.
The veto for central government is done by Cabinet and has not been used since 1987. That is because any Government that did so would pay a heavy political price for doing so.
As far as I know no elected local government entity has used the veto either. Again, because the Councillors who did so would risk losing their seats.
But No Right Turn highlights one local government entity that has used a veto. The Auckland Council Maori Statutory Board. They did a veto to prevent the release of information on the towns and districts where their board members resided.
It is appalling that an unelected body has the power to over-ride the Ombudsman. One can debate whether Councils or Cabinet should have the right, but at least as elected politicians they can be made to face consequences for doing so. The power of the Maori statutory Board to veto the Ombudsman should be removed from the law immediately.