Hi,
you need registration with the NZ Physiotherapy Board.
Have a look at their website; there is also a self-evalution tool with all the criteria.
The Physiotherapy Board of New Zealand > Registration - Overseas Qualified Physiotherapists
I know that the minimum qualification requirement is a 3 year full time bachelor degree with at least 1 year of clinical experience.
Hope, this helps for a start.
Cheers,
Fyzzio