From what I know bikes cannot be on footpaths unless they are shared paths. Under NZ transport law a path/footway seperate from any road for cars/bikes is still considered a it’s own road, just without the motor vehicle/bike provision, meaning that unless it’s marked as a shared path you can’t bike on it (the definition of a road is extremely broad from what I can tell). I think Christchurch has by-laws for this in Hagley park specifically, making every path there shared, but I couldn’t find anything similar for parks in general. I believe this is why certain parks have signs indicating that particular paths on them are cycle corridors, and also why the ccc on their smartview site only has certain park paths as shared paths and not all. I’m aware this is a massive technicality but the map should be reflective of what is legal.