New Zealand Cricket has referred the alleged racist abuse towards England paceman Jofra Archer by a spectator in last week's first Test to the police.

Hours after England slipped to an innings defeat in Mount Maunganui, Archer revealed on Twitter he heard "racial insults" from "one guy" in an incident that led to a wide-ranging inquiry from an apologetic home board.

The investigation included scrutinising CCTV footage, listening to audio, interviewing bystanders and obtaining material on social media although New Zealand Cricket has been unable to conclusively identify the individual.

However, New Zealand Cricket chief executive David White feels what it has gathered is enough to justify lodging a complaint with Tauranga police.

"What happened to Jofra was reprehensible and has led to a general upscaling of security around the area of racial abuse at all our international venues," White said.

"Should the person responsible ever re-offend, we believe we have enough information to link him to the Bay Oval incident."