"A bit disturbing hearing racial insults today whilst battling to help save my team, the crowd was been amazing this week except for that one guy, @TheBarmyArmy was good as usual also," Archer had tweeted after the conclusion of the first Test.
"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," NZC said in an official statement.
"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," NZC chief executive David White said in an official statement.
New Zealand clinched the Test series against England 1-0 on Tuesday after the second Test ended in a draw.