You say, 'It's been more than a month.' I'm afraid that these days, waits of this length and longer are nothing out of the ordinary. INZ and all the connected processes are struggling with huge backlogs.
INZ get NZ police certificates directly - the applicant isn't involved in that. Therefore, it MAY be that the reply from NZ police meant that they couldn't find a request from you for your information (because you haven't made one). In your place, I would tell your CO in an email what you've just said here, because it's up to him/her to follow it up.