I have consulted before. If you have an identity, you need to provide proof of overseas income and rental income, which are recognized in New Zealand. I remember that I need to provide your transfer records in China Bank for three months, together with the formal rental contract. There are also proof of pension/salary and proof of monthly expenses (this is usually the form you need to fill out when applying for a loan in New Zealand).
However, generally speaking, if you buy a house with overseas income, 80% can't get a loan, and the down payment should generally be controlled at around 1/3 before it can be approved.
Bank deposits can be used as one of the loan conditions.
That's about it. On the whole, it is quite easy.
Have a permanent identity, that is, follow my above operation. Generally speaking, ASB is relatively easy for overseas.