As a Contracted Screenwriter, what tax code are you?
As an Independent Contractor your tax code will always be WT and you will need to fill in an IR330C when contracted by any party
Further on tax for Independent Contractors from IRD:
Do you need to register for GST?
You must register for GST if your turnover (ie. income as a contractor) has or will exceed $60,000 over a twelve-month period. If you fall below this threshold you may still register for GST but you are not obliged to. Being GST registered means you can claim back the GST on any business expenses so many writers register as a matter of course. Link to registering for GTS
Do you need to set up a separate company?
No, you can run a business as a self-employed contractor and claim expenses through that. However, if you are doing more than just working for yourself or if are engaging or employing others to do work you may want to talk through the advantages of setting up a separate company with a tax agent or accountant.