Police say there are inconsistencies between statements they are getting and injuries a baby who died in Te Kūiti had.
The 10-month-old boy, Mustafa Ali, was brought unconscious to Te Kūiti Hospital on Saturday afternoon.
"Tragically, despite the best efforts of medical personnel, he was unable to be resuscitated," detective inspector Graham Pitkethley said.
Police have launched a homicide inquiry.
Mustafa's injuries were the result of violent blunt force trauma and did not appear to be accidental, Pitkethley said. A post-mortem was expected to take multiple days, he said.
"I believe someone who was with Mustafa has inflicted injuries on him."
Police believed his mother, father and two other people lived at the house, but they believed the two other occupants were not present during the day and had left early.
At this stage, police believed Mustafa's fatal injuries took place the same day his mother and father took him to hospital.
The parents had spoken to police but Pitkethley said he had concerns there were inconsistencies with the family's statements.
"Inconsistencies involving the statements from the people that we've spoken to, [which] don't seem to relate to the injuries as we would expect and so that's part of the scene examination, post-mortem and our inquiries," Pitkethley told Checkpoint.
"Any homicide inquiry is to reconstruct the event and then determine if a third-party is involved in that death.
"In short, the statements that we've obtained from family members are not consistent with what we believed caused the injuries."
Injuries suffered by a ten month old baby no accident - Police
Mustafa's father has denied any wrongdoing.
"Mustafa Ali is known to police in regards to a non-accidental injury previously that has been investigated," Pitkethley said.
Police were notified of this incident in October and Pitkethley said that inquiry was due to be completed shortly before Mustafa's death.
Pitkethley was asking for anyone in the community with information to come forward, including anyone who heard screams coming from the house.
"Te Kūiti is a small tight-knit community. There will be people who know the family and Mustafa and have had interaction with him, they may know relevant information that has occurred over the last 10 months - which is Mustafa's life - and also we know that it's been reported in the paper with regards to screams coming from the house on the Saturday.
"We know that it sounded like a female voice that was screaming from the house at that time, and again the investigation is working towards establishing what has occurred and I'm not going to go too much into the details of who we believe it is at this stage."
Non-accidental injuries on children were one of the most complex cases police could work on and complexities were present in this case too, he said.
Police will continue to speak to family members and were working to reconstruct Mustafa's entire life, from birth until death.
Oranga Tamariki said it had been notified of Mustafa's death.
Oranga Tamariki service delivery deputy chief executive Rachel Leota confirmed to RNZ the organisation had prior involvement with the family.
"As this matter is subject to an active police investigation, we cannot go into further details.
"Oranga Tamariki continues to assist police in trying to understand the circumstances that led to the death."
The death was "a huge shock to the community", Waitomo District Mayor John Robertson told Morning Report.
"We have our tragedies from time to time, but no community wants to see a 10-month-old baby apparently suffer like this baby did."
Te Kūiti had a population of 4500 people, he said.
"A lot of sympathy goes to those who knew the child but shock at the fact that this could happen in our community."