The Independent Police Conduct Authority had been notified the man had been in custody prior to his death, as was ''standard procedure,'' the statement said.
A source told the Otago Daily Times Willyams fell down the stairs after he was asked to leave the bar for "inappropriate behaviour" towards staff.
He was believed to be "sober" when he was removed from the bar.
Carousel owner John Devereux said he believed Willyams had fallen down the stairs at the entrance to the bar after its one-way-door policy began at 3am.
As of last year Willyams was listed as retired and living in central Dunedin.
He was not a regular at the bar and not known by staff.
The police inquiry into his death concluded it was not suspicious, and the case has been referred to the coroner.
Dunedin City Council customer and regulatory services group manager Adrian Blair said no action was being taken by the council with regards to the bar's alcohol licence.
"If any action was to be taken in the future in relation to this incident, this would sit with police.''