Photo: RNZ
On December 2, police were notified that the girl had been brought into hospital by her family.
She had a broken leg - an unusual injury for such a young baby.
Her condition is improving, police said.
Detective Senior Sergeant Steve Wescott said the investigation has "uncovered contrasting narratives on the circumstances, and officers are appealing to the community to assist with understanding exactly how this baby girl bore such serious injuries to come forward".
He thanked people who have come forward so far.
