The current rule
New Zealand Daylight Time begins at 2:00 a.m. local on the last Sunday in September and ends at 3:00 a.m. local on the first Sunday in April. Standard time is UTC+12:00 and daylight time UTC+13:00, giving New Zealand one of the earliest clocks on Earth. The Chatham Islands sit 45 minutes ahead of the mainland and change on the same dates.
Where the idea came from
The modern concept of daylight saving was first set out in a paper delivered to the Wellington Philosophical Society in 1895 by George Vernon Hudson, a New Zealand entomologist who wanted more daylight after work to collect insects. He proposed a two-hour shift. It was received poorly and went nowhere for two decades, until wartime fuel shortages made the idea suddenly attractive in Europe.
A 45-minute offset
The Chatham Islands run on UTC+12:45, and UTC+13:45 in summer. Along with Nepal at UTC+05:45, they are among the very few places on a quarter-hour offset, and they are a standard test case for date-handling code that assumes offsets divide evenly into hours.