Can New Zealanders marry their cousins? What documents refer to this in Law?

Hello.

The relevant law is Section 15 of the Marriage Act of 1955. That
section is reproduced on the back of New Zealand Form BDM60 - Notice
of Intended Marriage.

Download the form from the New Zealand Department of Internal Affairs:
http://www.dia.govt.nz/Pubforms.nsf/URL/bdm60.pdf.pdf/$file/bdm60.pdf.pdf
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Or  view an html version cached by Google:
http://216.239.53.104/search?q=cache:fewcHWfwO64J:www.dia.govt.nz/Pubforms.nsf/URL/bdm60.pdf.pdf/%24file/bdm60.pdf.pdf+&hl=en&ie=UTF-8

Here are the rules on whom a woman may marry (the man's rules are a
mirror image of these):

Forbidden Marriages
A woman may not marry her -
(1) Grandfather
(2) Grandmother?s husband
(3) Husband?s grandfather
(4) Father?s brother
(5) Mother?s brother
(6) Father
(7) Stepfather
(8) Husband?s father
(9) Son
(10) Husband?s son
(11) Daughter?s husband
(12) Brother
(13) Son?s son
(14) Daughter?s son
(15) Son?s daughter?s husband
(16) Daughter?s daughter?s husband
(17) Husband?s son?s son
(18) Husband?s daughter?s son
(19) Brother?s son
(20) Sister?s son

A cousin would not fit into any of the prohibited categories.

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search strategy:
marriage, prohibited, site:nz
"marriage act", site:nz
forbidden marriage, "marriage act", site:nz

I hope this helps.