Human Rights Act 1993, ss 42, 44 Official Information Act 1982, s 12
Government and private organisations can ask you to provide proof of your identity when you’re dealing with them, but you shouldn’t be asked to provide more proof than a cisgender person.
If you think an organisation is treating transgender and cisgender people differently and want to take action, you could ask to see the organisation’s policy for asking for proof of identity. If they are breaching the policy, or if they have an unfair policy, you can use this information to complain to the Human Rights Commission.
If the organisation is a public service, you can ask for the information formally under the Official Information Act 1982 (see: “Getting information from the government”). If you’re dealing with a private business, getting their policies can be more difficult, because there are different rules about what information they have to make publicly available. For support you can contact your local Community Law Centre.