U.S. citizens and resident aliens are subject to U.S. federal
taxation, irrespective of whether they are working in the U.S. or in a foreign
country. So your income earned in New Zealand will be subject both to U.S.
federal and New Zealand taxation.
However,
there are provisions in the U.S. tax code to mitigate double taxation of income
earned by U.S. citizens and residents working abroad - if your tax home is abroad and your physical presence outside of the U.S. allows you to meet the tests, you can qualify for a
foreign earned income exclusion under 1 of 2 tests, the Bona Fide Residence
Test or the Physical Presence Test, as well as a foreign housing exclusion or
deduction, for your New Zealand housing costs. You can also take a foreign
tax credit for the New Zealand taxes paid on your unexcluded income earned there, to
the extent it is double taxed both by New Zealand and the U.S.
TurboTax
supports filing Form 2555, Foreign Earned Income,
to calculate your
foreign earned income exclusion and foreign housing exclusion or deduction, as
well as Form 1116, Foreign Tax
Credit.
The Deluxe,
Premier and Self-Employed versions of TurboTax Online all support Form
2555 (not Federal Free), as well as all versions of TurboTax
Desktop, for Windows or Mac.
Please see
the following TurboTax FAQ, "What are Forms 2555 and 2555-EZ used
for?", for instructions on how to enter information in TurboTax about your foreign earned income, even if not reported on a Form W-2:
https://ttlc.intuit.com/replies/3301984
To see where
to enter in TurboTax Online foreign income taxes which you paid or
accrued in 2016, for purposes of claiming the Foreign Tax Credit on Form
1116, please see the following TurboTax FAQ, "Where do I enter the foreign
tax credit (Form 1116) or deduction?":
https://ttlc.intuit.com/replies/3302405