Detective Senior Sergeant Greg Turner said 14 investigators were working on the case and police were working closely with the family.
A neighbour who is also a relative of the baby's mother, Shannel Tata, told the Herald she went into the child's bedroom to check on him about 10.30am last Thursday and saw he was struggling to breathe.
She took him from his cot and phoned an ambulance.
She said Ms Tata was devastated.
St John acting team manager for the Taupo district, Steve Lynch, said he manually ventilated the child at the scene before he was taken to hospital with his mother by his side.
"He had gone into respiratory arrest. The child had a pulse and his heart was still beating but he wasn't breathing for himself."
Mr Lynch has been interviewed by police about his part in the rescue.
Another neighbour said she saw the baby being put into the ambulance.
"The mother was yelling 'why isn't he breathing?', 'Why isn't my baby breathing?'"
Ms Tata is believed to have two other young children, a boy and a girl. She had her two youngest children with her current partner, Adam.
Child, Youth and Family acting regional director Don Horsefield said the baby had been known to the department.
"The death of a baby is always tragic, and my deepest sympathies go to those who loved this baby.
"CYF is assisting the police and working with the baby's family."
