If you are a New Zealand tax resident you are taxed on your "worldwide income" - that is income from New Zealand as well as from other countries. If you receive overseas income while you're a tax resident of New Zealand, you'll need to declare it to us on an Individual tax return (IR3). Generally New Zealand will give a foreign tax credit for any foreign tax paid but the credit is limited to the amount of NZ tax that's payable on the overseas income.

When am I considered a tax resident of New Zealand?

You are a tax resident in New Zealand if you:

-are in New Zealand for more than 183 days in any 12-month period and haven't become a non-resident, or
-have a 'permanent place of abode' in New Zealand, or
-are away from New Zealand in the service of the New Zealand government.

**Note
Even if you maintain ties (or even a physical home) in other countries you can still be a New Zealand tax resident. As long as you have a permanent place of abode in New Zealand you'll always be a resident.
This test also overrides any rules about the number of days you're here - so even if you're out of New Zealand for more than 325 days you'll still be a tax resident if you have a permanent place of abode in New Zealand.**

http://www.ird.govt.nz/international/residency/personal/personal-tax-residency-index.html

Double Tax Agreement - Kor - NZ
http://www.legislation.govt.nz/regulation/public/1983/0005/latest/096be8ed8077f668.pdf