According to the 1986 document of the Conservation Status of New Zealand Wildlife, both L. colubrina and L. laticordata have occurred in New Zealand.
laticordata in that document (and others that had quoted it) is a misspelling of
laticaudata and it was actually a misidentification.
However, oddly enough,
Laticauda laticaudata has been recorded in New Zealand recently and there are now four species of sea snake on the NZ list, although it doesn't really change anything as the two latest species are only known from one specimen each.
Up until 2005 there were two species recorded from NZ, namely
Pelamis platura (aka
P. platurus) which is the most commonly-recorded species, and
Laticauda colubrina which is only occasional.
In 2005 there was a taxonomic revision of
L. colubrina which resulted in some new species being named, one of which was
Laticauda saintgironsi. This new species is more or less found only around New Caledonia but during the research for the revision it was discovered that one of the older
L. colubrina specimens from NZ was actually of this new species. So the NZ list got bumped up by one.
Some time very recently (definitely after 2010 but I don't know the exact date or locality because I can't find any publication about it) an individual of
Laticauda laticaudata reached NZ. And that makes the fourth species.