The number of babies dying each year from sudden unexpected death in infancy, or SUDI, remains unchanged at 10.
The figure is contained in the latest report from the Perinatal and Maternal Mortality Review Committee.
The report says there were 700 perinatal-related deaths in 2008, among total births for the year of 65,872.
It says the rates were consistent with the previous year, and similar to those in Australia and Britain.
There were 379 stillbirths - about six for every 1,000 births.
The committee says the stillbirth rate is of concern and needs closer study.
It says Maori and Pacific women are more likely to have a stillbirth or a neonatal death, particularly in poor areas.
Almost half of women who had stillborn babies, and 45 percent of mothers of neonatal deaths, were overweight or obese.