Acting Detective Sergeant Matt Jones said people reported they recognised the voice of a caller who used the driver's cell phone to call Green Cabs after the incident as a relative of the driver.
"This information, together with a number of consistencies in other information gathered and out-of-character behaviour by the arrested man, has led police to the conclusion that this is a false complaint," he said.
The investigation had taken up a lot of police time and resources, police said.
Police said Green Cabs had co-operated with the investigation, and that the man was no longer employed by the company.
He will next appear in the Manukau District Court on June 17.