"We want to build a full picture of the circumstances which led to emergency services being called to the address," he said.
"A post-mortem examination is due to take place later today which we expect will provide us with further information to progress our enquiry.
"Police are keeping an open mind about the involvement of other people, and we cannot rule out further charges being laid as our enquiry continues.
"This is a tragic death of a young baby and the investigation team is very focussed on establishing exactly what happened to her."
Forensic specialists were continuing to examine the scene at the Raumati Beach address today.
A further scene examination at a Waikanae address was completed last night.
The identity of the baby girl will be released once all next of kin have been informed.