Rural and Urban Fire is now managed by Fire and Emergency New Zealand. You can apply for a Rural Fire Permit on the Pumicelands website or via the Apply for it button to the right.
Under the Health Act 1956, Council will respond to complaints from the community regarding smoke nuisances. Council staff are able to require outdoor fires be quenched if it is deemed that the smoke nuisance from the fire is likely be offensive or cause potential health concerns. This relates to both rural and urban fires for waste, refuse, rubbish and cooking.
More information on rural and urban fire constraints is available from Waikato Regional Council's website here.