A United States embassy official said Saturday the man had left New Zealand.
The following day New Zealand's ministry of foreign affairs sought, on behalf of law enforcement, a waiver of his diplomatic immunity.
Police said they were called to an incident in Lower Hutt, on Wellington's outskirts, in the early hours of March 12, which "involved an individual from the United States embassy in Wellington". It is understood the diplomat has since left the country, although New Zealand police said the investigation was "active".
However, the New Zealand government makes it clear foreign diplomatic staff must abide by the law and "waive immunity should MFAT request it if there are allegations of serious crimes".
White left the address with a broken nose and a black eye before police arrived.
They said they were working with the Ministry of Foreign Affairs and Trade, which asked the USA to waive immunity on Monday.
The spokesman says the U.S. is communicating with New Zealand authorities.
A U.S. diplomat has been ejected from New Zealand after the USA embassy in Wellington refused to waive his immunity, according to media reports on Sunday.
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"This occurred in the afternoon of Monday 13 March, in accordance with New Zealand's policy to request a waiver of immunity when Police wish to investigate allegations of serious crimes".
Mr McCully says he is satisfied with the way the ministry has conducted the process.
New Zealand Foreign Minister Murray McCully called the decision "disappointing" in a written statement.
"We take seriously any suggestion that our staff have fallen short of the high standard of conduct expected of US Government personnel", she said.
McCully said the USA had stated it always fully investigated all allegations involving its diplomatic staff.
The US embassy in Wellington - which is without a permanent ambassador after President Barack Obama's appointee was recalled by Donald Trump's administration in January - said it did not comment on the specifics of matters under investigation.