OK, if its just the rental income you are being taxed on, no problem, but, the New Zealand IRD also considers that you should continue to pay NZ tax if you have an "enduring relationship with New Zealand" even if you have been working overseas for a significant period of time. In terms of taxation agreements, the tax you pay in Singapore is offset against the substantially larger NZ tax bill. In one of the cases that actually came to court, a gentleman had been working in Fiji for eight years, but it was still considered a tax resident in New Zealand. The only other country that has a similar point of view is the US: if you are a US citizen (or greencard holder) you are taxed in the US no matter where you are in the world. They do give you a tax free allowance of (I think) the first $75,000. NZ gives no such concession.
Things that would probably make the New Zealand IRD consider that you have an enduring relationship with New Zealand are:
1. Spending more than 40 days in NZ in any year
2. Owning
property in New Zealand that you have ready access to. For example. its OK to have a rental property as an investment, but, if there is a room in that property that you can use whenever you are in NZ, then that gives evidence that you have that enduring relationship. If you own a holiday property in NZ, that can also be assumed to be the basis of an enduring relationship
3. Working overseas on assignment for a NZ company
4. Allied with 3, having a job to come back to, or if you are on leave of absence or sabbatical.
5. Having items in storage in New Zealand: this is evidence that you intend to come back some time.
5. Having dependents in New Zealand
If you ask me this is all kind of dumb, because it forces New Zealanders who are going overseas to sever all ties if they are moving to a low tax regime. You would have thought they would encourage NZ'ers overseas to keep up their ties, and keep up their relationship.
What you are supposed to do when you leave NZ is fill out a questionnaire on the IRD website, and they will then tell you in a couple of weeks what your tax status is. We were alerted to this by our accountant in NZ, so we sorted out our affairs accordingly, filled out the form and got the right response from the IRD. We do still have a property in NZ that we rent out on a long term basis, which apparently is OK.
If the assessment you received is only in respect to income on your rental property, then its a pretty straightforward situation. If its to do with your Singapore income, then you are going to need some professional advice to address the situation. I am happy to pass on our accountant's details if you would like them