They ignored advice given at Hawke's Bay Hospital and were caught multiple times persisting with this behaviour.
Health professionals issued a special sleeping cot called a Pepi-Pod because of the co-sleeping habit, and because the baby was of a low birth weight, and was premature.
A Pepi-Pod is rectangular with sides which allowed parents to sleep babies safely alongside them.
It was found propped against the wall when the baby was left alone at the hospital.
In October 2013, emergency services also found it unused and on the floor when they were called to the house the morning the baby was found unresponsive.
The mother put her baby girl to sleep in a queen-sized bed the previous night and returned with her 2-year-old son for bed about an hour later. She woke early the next morning to find her daughter unresponsive, her son's arm laid over the baby's face. A post mortem examination established cause of death to be Sudden Unexpected Death in Infancy (SUDI) due to an unsafe sleeping environment, attributed to probable accidental asphyxia, smothered by the baby's sibling's arm.
She told police she had used the Pepi-Pod at times, but not often because it was annoying to lift on and off the bed.
The police are now using her case as an example to other parents of the importance of safe sleeping practices.
Detective Sergeant Tim Smith said the death was preventable. "It is not our aim to victimise parents after the tragic death of a child and any prosecution is taken after careful consideration of all the circumstances".
The dangers of babies co-sleeping with parents were well-known and health agencies were proactive in their efforts to educate families about the issue.
"There is a responsibility on parents to ensure safe sleeping advice is adhered to but we would also like to see all parents, grandparents, whanau and family take responsibility for ensuring safety around co-sleeping," Mr Smith said.
"As parents we have social and legal obligations to ensure the safety of our children. These obligations include making sure that we provide our children with a safe sleeping environment."
The baby's parents had been given information on co-sleeping and other risk factors when their baby was born premature.
A family safety plan had been prepared for the couple also. The detective said: "In situations such as this where there has been a significant departure from the standard of care expected of parents, criminal charges will be considered".
This comes just a day after the Child Youth and Youth Mortality Review Committee report was released that said over the past five years there were 42 fewer SUDI deaths among Maori families which statistics showed were most affected.
Despite the Safe Start Education programme which taught parents how to safely sleep their children, 40 per cent of New Zealand families still did not have safety checked sleeping arrangements for their baby.