Yes, it has a constitution, that is why it a constitutional monarchy. But it is not one document but a collection. It is similar to Englands.

The first parliament in New Zealand was called the 1st New Zealand Parliament. It commenced in 1854, two years after the British colonial power sought to give the colony representative government by enacting the New Zealand Constitution Act of 1852.

The treaty of Waitangi (in New Zealand)

Kenneth John Scott has written:

'The New Zealand constitution'

New Zealand has a parliamentary system because it was once a British colony. British settlers began campaigning for self-government right from when the first settlers began to arrive in the 1840s. In 1852 Britain's parliament passed the New Zealand Constitution Act which created the New Zealand Parliament (then known as the General Assembly), and the first elections were held in 1853.