He confirmed no charges had yet been laid, and would not comment further on whether charges were possible. "I don't want to even go there at this stage."
Police were not releasing any details relating to the identity of the four-month-old boy but Mr Greig said they are "very happy" with the co-operation of the family which had been hit by the tragedy.
"This is obviously a very distressing time for them and overnight it has become much more distressing," he said on Saturday. Police were hoping the body will be released to the family today, and the name of the child would also then be released.
The boy was rushed to Wairoa Hospital by ambulance from an address in Lucknow St, Wairoa, mid-morning on April 13, and transferred later that day to Hawke's Bay Hospital in Hastings, and the next day to Auckland's Starship Children's Hospital, where he died.
Sources in the town have told Hawke's Bay Today few in the area seem to know or have heard anything about what happened.
The house was empty this week. Several residents in the town said no one was saying anything about it.
"We only know what we read in the newspapers."
Sources have also told Hawke's Bay Today that another child in the family was cared for by friends for some time as the family dealt with the trauma, and as police closed their home as an investigation scene.
Police were also working with Child, Youth and Family on the matter, he said, but CYF central regional director John Langley confirmed: "None of the children in this family are in our care."
The police team had largely taken a break yesterday but was expecting to continue active inquiries today.
