From the relevant page of the Foreign & Commonwealth Office website:
"Ensure that your passport is valid one month beyond the date of expiry of your visa. If you intend to stay in New Zealand as a visitor you are entitled to a six month stay visa-free but should ensure that your passport is valid for one month beyond the date of your visa-free stay"
Suggest you check with your travel agent though I suspect Buenchico is correct. If it were me I wouldn't take the risk of the passport running out so would have it renewed soonest.
Ill-health and accidents happen and you wouldn't want to find yourself in NZ after June for either of these reasons passport-less.