New Zealand - Criminal Background Check

You can apply to the Privacy Unit at the Ministry of Justice for a copy of your conviction record, the document can take 20 days to be issued.
More information on the document can be found here: http://www.justice.govt.nz/privacy/

Application form: http://www.justice.govt.nz/privacy/request-by-individual.pdf

Once you have received the police statement, it must be authenticated / stamped by the Department of Internal Affairs. Here is a link to their website:
http://www.dia.govt.nz/apostille