Police could not comment on how the injuries were sustained because they were still investigating and it could prejudice any future court action.
''A significant investigation has been undertaken during the last three weeks by a team of experienced investigators from the Dunedin police child protection team working closely in partnership with Child, Youth and Family and the [Southern] District Health Board,'' Det Insp Fitzgerald said.
''During this investigation, a number of persons have been spoken to from the wider family across New Zealand.''
Despite the lack of arrests, the investigation was nearing completion.
''The information police have obtained to date has been helpful in establishing the cause of the injuries and the investigation is now in its final stages,'' he said.
Police could not comment on the number of suspects or the extent of their involvement. St John South Island region communications adviser Ian Henderson said St John was alerted to the incident at 9.52am on April 10.
Two ambulances and a St John prime response in a medical emergency (Prime) responder were sent to a private residence in Palmerston after reports of an injured baby.
The girl was taken to Dunedin Hospital's emergency department by ambulance in a serious condition, he said.
