After the completion of the first Test at the Bay Oval which New Zealand won by an innings and 65 runs, Archer had claimed that he was subjected to "racial insults" by a spectator following which NZC and Kane Williamson had tendered an apology.
"Information gathered from an inquiry which included studying CCTV footage, listening to audio, interviewing bystanders and obtaining material on social media has been incorporated in the complaint," said NZC in an official statement.
NZC chief executive David White said: "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," he said.
"Should the person responsible ever re-offend, we believe we have enough information to link him to the Bay Oval incident."
White confirmed that, if a conclusive identification was forthcoming, NZC would seek to trespass the offender from all its international venues for a lengthy period.
New Zealand clinched the two-match series 1-0 after the second Test at the Seddon Park in Hamilton ended in a draw on Tuesday.
The Black Caps will now head to Australia for a three-match Test series. The series will begin with a day-night game in Perth from December 12. The second Test begins on Boxing Day at the MCG and the final fixture will be played at the SCG from January 3, 2020.
( With inputs from IANS )