N.Z Certificate of no Impediment to Marriage .

Hi, this should be done in NZ. Please note if the document is a power of attorney, it must be notarised by a Notary Public in New Zealand before you send them to the Department of Internal Affairs of New Zealand. Then, it should be sent to the Consulate-General for the finial authentication.

I have a Certificate of No impediment to marriage from Department of Internal Affairs . Do I now take this to The the Embassy here in Christchurch ? Do I take it where you apply for China visit permit

You can bring it to the nearest consulate or embassy for authorization. Here is the detailed procedure:
http://christchurch.chineseconsulate.org/eng/lsfw/lsrz/P020120718214206587501.pdf