The NZME investigation found that more than a dozen KiwiSaver providers had made direct investments totalling $43 million in companies blacklisted by the Government-owned New Zealand Superannuation Fund for making the banned weapons.
The funds in question are widely popular, with more than 1.8 million New Zealanders making regular contributions to them.
Further investigation, by both NZME and Radio New Zealand, found the number of exposed providers widened considerably once underlying holdings of index funds were taken into account.
The unfolding scandal has led most providers to announce a review of investment policies and several - notably Grosvenor and AMP - to announce plans to divest controversial holdings.
Asked how police were treating the complaint, a spokesperson said: "Police are making inquiries with other agencies to gather more information. This will be assessed as appropriate in due course."