There are three available response options: number born alive; none; or object to answer this question.
The petition was launched by baby-loss support group Sands New Zealand and calls for Statistics New Zealand to modify the question in future because it upset some parents of the estimated 500 babies born dead each year.
"Mothers who have had a stillborn regularly report distress when asked how many children they have in social situations," said Dr Cathy Buntting, chairperson of Sands. "Now, in the national Census, they face the same upsetting predicament.
"They are asked how many children they have given birth to, but there is no room for them to acknowledge their babies who were born, but who were tragically not born alive."
Mother-of-two Buntting, from Morrinsville, Waikato, has had one baby stillborn.
"These babies might not matter to fertility statistics, but they do and will always matter to the mothers who bore them and the fathers who miss them."
A birth certificate is issued for babies stillborn after 20 weeks.
"In addition, the number of babies lost before 20 weeks runs into thousands annually, and this is just as distressing," Buntting added.
The petition has drawn criticism from people on a popular Trade Me internet forum about parenting. They think it is an over-reaction by some to the Census question.
But George and Holly Poole, whose first child Darcey Mae was stillborn at 36 weeks and five days last October, were distraught when they saw the Census forms.
"Our little girl was a fully formed human being who would respond to voice, hiccup and touch," said George, from Bulls. "For her not to be recognised as a New Zealander or counted in the Census is as though she never existed, which is hurtful and insulting."
Statistics spokesman Gareth Meech was aware of the petition.
"We have a lot of sympathy with parents of babies that have sadly passed away before they were born, and who may feel uncomfortable answering the question.
"We will have increased public consultation around the issue before the next Census."
Staff delivered 6.4 million Census forms by Tuesday night, including 1.8 million dwelling forms and 4.6 million individual forms for a population estimated at 4.46 million.
Census spokeswoman Vikki Carter said 35 per cent, or about 2.2 million, were expected to be returned online. Collectors would pick up forms until March 17.
Failing to fill in a form can lead to a $500 fine.
