An infant who died from serious injuries early on Sunday was Hail-Sage McClutchie from Hamilton.
The 22-month-old toddler died in Waikato Hospital but a police said results from a post-mortem were unclear and they were waiting for further tests to decide how she had died.
She was taken to hospital from an address in Morrinsville on Saturday afternoon.
Police were treating the death as suspicious and were still speaking to people about how she received her injuries. They also warned people not to come to unsubstantiated conclusions.
They said it could be several days before they knew the precise cause of death.