Police are looking into previous reports of domestic violence at the home of a four-month-old boy critically injured in South Auckland nine days ago.
The baby is in a critical but stable condition at Starship Hospital, and Dave Pizzini, the officer in charge of Counties-Manukau's child abuse team, says it is too early to know the extent of any brain damage the baby suffered.
Mr Pizzini says doctors report that he is making slow progress.
Police are still interviewing the baby's relatives and neighbours.
Meanwhile, police are continuing to investigate the death of a newborn baby at a rural property in Te Puke on Friday morning.
They have questioned medical staff as well as members of the baby's family, including the 17-year-old mother, and say family members are co-operating fully.
Police say a post-mortem has proved inconclusive, adding that the death appears to be a case of a hidden pregnancy and birth.
They say further work will be required to identify the cause of death and will seek expert medical advice.
No charges have been laid, but police say they will seek expert medical and legal advice before any decision.