This document details what level of rigger is needed for specific tasks and has been pulled from the LPA Live Rigging Hazard guide (can be found in the WHS Resources on the intranet).
In short, if you are hanging lights, PA, set, etc. off installed systems (fly bars, pods, installed scaffolding) or building anything that doesn't move by mechanical means (needing a motor or chain block), you don't need a rigger. If you are doing any hanging in The Parade/Reg, you will likely need a fly supervisor.
Please note, this is a guide only. For more detail and nuance, come and talk to tech ops.