After both deaths the children's mother, now 21, told police she put them to bed in the morning after they had been fed.
When she went to check them a short time later they had stopped breathing.
The baby girl died on May 15 and since then a team of detectives have been investigating.
A scene examination has been carried out at the house where the girl and her brother died and their parents have been formally interviewed, Stuff.co.nz reported.
It is understood both parents denied any wrongdoing.
Detective Senior Sergeant Greg Cottam said as part of the police inquiry investigators had looked at a disorder known as Munchausen syndrome by proxy.
Also known as "medical child abuse", the disorder is relatively rare and involves a parent or other adult closely involved in a child's care making up or exaggerating symptoms.
It is a mental illness and requires treatment.
Tests have been carried out to identify if there were any genetic factors that led to the children's deaths. Results were expected back in several months.
The woman's six-week-old son stopped breathing at home on March 6 last year and emergency services were called by he could not be revived.
Mr Cottam said the woman also had a four-year-old son. She had voluntarily given up custody while the deaths of his siblings were investigated and Child Youth and Family were involved.
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• Lifeline: 0800 543 354 (available 24/7)
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• Depression helpline: 0800 111 757 (available 24/7)
• If it is an emergency and you feel like you or someone else is at risk, call 111.
