Hinekawa was taken to hospital by her parents, Tiffany Topia and Tom McGregor, after she stopped breathing on January 12. An autopsy revealed she died from a head injury.
Detective Senior Sergeant Neil Forlong said a "detailed picture" of Hinekawa's care arrangements since her birth still had not been confirmed.
That included whether there was a formal arrangement for members of the extended family to care for her and her siblings.
Mr Forlong said the number of houses she lived in - and where she was fatally injured - would need to be established.
Police have already searched two homes, one in Wanganui and the other in South Taranaki, and taken items for testing.
CYF's general manager of operations, Marama Edwards, said Hinekawa's sisters were placed with a CYF caregiver when they left hospital yesterday. Their 5-year-old brother is already in CYF care.
Deborah Morris-Travers, advocacy manager for Barnardos, said it was vital for parents to have the opportunity to create attachment with infants.
"It's really important for all parents to be supported in those early weeks after a birth to create that attachment with their children. Anyone who has the responsibility or care of a newborn certainly needs support and [to] be equipped with the knowledge of the way to care for a child.
"It's highly stressful for anyone so certainly would be for someone caring for a newborn or infant that wasn't their own child."
