Everyone working in New Zealand for any period must be a New Zealand or Australian citizen, and Australian permanent resident, hold a New Zealand residency permit, or a valid work visa (Australians have the automatic right to work in New Zealand). This is the law, and the responsible government department, Immigration New Zealand, is required to implement it.
Visiting producers, directors, cast and crew must apply for a Temporary Work Visa before they come and work. Usually the production arranges the work visas on behalf of the crew. These requirements apply equally to ordinary employees, independent contractors and freelance crew. In Immigration New Zealand documentation the word employee also applies to contractors and freelance crew.
The most common screen crew visa is called an Entertainers Work Visa.
To assist Immigration New Zealand interpret the law, they work within rules laid out in the INZ Operational Manual. The part that specifically relates to temporary entry for screen crew Immigration Instructions - Temporary Entry 2. The current version is dated 31 April 2021. Information on this The Screen Guild website is a highly simplified summary, and you should refer to the full INZ Operational Manual or the Immigration New Zealand website to get the full detailed picture.
Section W3.1 of Immigration Instructions - Temporary Entry 2 requires, among other things, that the producers show that the crew they want to bring in are manifestly essential to the production, or that they do not put at risk engagement of New Zealand professionals, or that the producer has appropriately looked at engaging New Zealand professionals.