Double taxation agreements are in place so an individual does not get taxed twice. This mainly affects a person in two ways. They either get relief in the other country on tax already paid, or under Article 4 of the OECD Double Taxation Treaty, both countries agree that tax will only be handled in one of the countries on certain types of income.
The 41 day issue is in place because NZ consider that once a person is tax resident, they will remain tax resident for a period of 365 days – 41 days. Thus, if a person has been resident for the 41 days, they can normally assume they were resident for the complete tax year. However, as soon as the person leaves for longer than that period, they will have been non-resident from that time minus that period. i.e. rolled back.
In order to satisfy the tax resident qualification for an RRV, you will need to show evidence in official documentation from the NZ IRS. In a similar way to a P85 in the UK, you will fill out a tax questionnaire for the NZ IRS. This details things like connections in NZ, etc and is used to determine your enduring relationship with NZ. They will send this information to the NZ Immigration Service too, but you will need them to send you the outcome so you can present it in your RRV application.
The application can be made from overseas, just make sure you have all your paperwork in order.
It gets very complicated, but be sure that this is something you want to do. The implications are that you will probably become resident for tax reasons going fwd, even though you are no longer in NZ. At least if you state that you are only going to be away from NZ for a few years.
Also, at least with the UK, unless you have been away for 3 years, you will still be an “Ordinary Resident”, upon your return, so you will need to show all your financial affairs in NZ on the Foreign Section of your UK return. This also gets onto Domicile issues, which are another story, but read the IR20 leaflet from the UK IR.
If you go this route and become Resident for Tax Reasons in NZ, you will be taxable on your worldwide income in NZ when you leave.