You can apply if:
the child was removed from New Zealand to another contracting state in breach of the applicant’s “custody rights”, and
those “custody rights” were actually being exercised when the child was removed, or would have been if the child had not been removed, and
the child was usually resident in New Zealand immediately before being removed.
Care of Children Act 2004, s 97
For the purposes of the law relating to child abduction, “custody rights” mean rights relating to the care of the child and, in particular, the right to determine the child’s place of residence. The New Zealand courts have decided that these custody rights also include the right to contact, access, or visitation with a child, that is, even if you weren’t providing day-to-day care for the child, if you did have the right to contact or visit the child, you can still apply to have the child returned.