From the New Zealand Parliament website:
Petition requesting citizens initiated referendum – what happens next
On 12 March, a petition requesting that a nation-wide referendum be held was presented to the Clerk of the House of Representatives.
The petition proposes that a referendum be held on the following question:
Do you support the Government selling up to 49 percent of Meridian Energy, Mighty River Power, Genesis Power, Solid Energy and Air New Zealand?
Under the Citizens Initiated Referendum Act 1993 the Clerk has the role of certifying whether the petition has been signed by at least 10 percent of registered electors as at the date received. If this threshold is met a referendum must be held.
Scrutiny of petition
The Clerk is responsible for scrutinising the referendum petition and has two months to certify if the petition has enough signatures.
If a preliminary count of signatures indicates that at least 10 percent of eligible electors may have signed the petition, a sample of signatures is checked. The sample to be checked is determined by the Clerk with the assistance of the Government Statistician.
The Clerk then gives the sample of signature details to the Chief Registrar of Electors, who checks them against the electoral roll and reports the result of this check to the Clerk. The Clerk, with the assistance of the Government Statistician, then considers the results of the check and determines whether the petition has enough signatures to succeed.
Resubmission of petition
If there are not enough signatures, the petition is certified as having lapsed and returned to the promoter, who may, within two months, resubmit the petition to the Clerk for another check to be made.
Presentation of successful petition to the House
If the Clerk is satisfied that a petition or resubmitted petition has been signed by at least 10 percent of eligible electors, it is certified as correct and presented to the House on the next sitting day. The petition is then referred to a select committee for consideration and report.
Holding a referendum
The presentation of a successful referendum petition to the House leads to the holding of an indicative referendum on the question set out in the petition. In principle, the referendum must be held within 12 months of the presentation of the petition to the House, unless the House passes a resolution postponing the referendum that is supported by 75 percent of members.
The referendum may be conducted by personal voting or postal voting. The decision on how the referendum will be conducted is made by the Governor-General by Order in Council within one month of the presentation of the petition to the House.