When you're dropshipping, you work as a middleman for your customers and your (dropship) supplier. Any taxes charged to you by your dropshipper will have to be charged to your customer. Usually, the dropship supplier charge you with sales tax if you're based in the same location as them. In your case since you're in New Zealand, you will not be charged with sales tax. However, if your customer is in the US and your dropship supplier is in China, you may be charged with custom duties for importation. You will then have to pass on the charges to your customer so it's best to clarify the setup with your dropship supplier before selling their items online.
Hope this clarifies your concern.