The incident happened Saturday evening.
A woman was treated for minor injuries and a man was uninjured, according to local media reports.
MORE: Anne Kirkpatrick sworn in as Oakland's new police chief
New Orleans police say a breathalyzer test returned a result of zero.
The investigation is now being turned over to state police for review.
MORE: Fired Oakland Police Chief Anne Kirkpatrick levels accusations at Mayor Libby Schaaf, police commission
Fired Oakland Police Chief Anne Kirkpatrick breaks silence
Kirkpatrick was Oakland's police chief from 2017 to 2020.
She now serves as New Orleans Police Superintendent, which is their equivalent of police chief.