Committee chairman Nick Baker recommended blood-testing parents after such unexplained deaths if there had been profound negligence and parents were suspected of drinking alcohol.
Last week, an East Coast couple were sentenced after being found guilty of endangering a baby's life. The 10-week-old boy died after being put to bed with his mother, who had been drinking heavily.
Two years ago, a Rotorua woman was jailed after her 2-month-old boy died while sleeping with his heavily intoxicated mother in the back of a car. The baby slipped under her arm and suffocated.
Dr Morreau said blood-testing parents could help highlight risks around sleeping with infants and alcohol consumption.
However, such legislation would be a minor part of a much larger battle around safe sleeping and parenting practices.
"The bigger issue is the need for New Zealand to recognise that it has a problem not just with SUDI, but also with multiple other health, educational and welfare problems, affecting 10-20 per cent of our children.
"As a country, there is urgent need for us to divert substantially more resources to working with families and supporting effective parenting if we seriously want to make a difference here," Dr Morreau said.
Children's Commissioner Russell Wills backed Dr Baker's recommendation - but specified it would only be appropriate in suspicious cases.
"Sometimes adults simply refuse to follow advice and they choose to endanger their children," Dr Wills said.
"They drive drunk with the kids in the car, they don't ensure that kids wear the seatbelt that's fitted, they choose to co-sleep with a baby when they're drunk, even when [support networks] are in place."
These parents should to be held accountable for their actions and blood-testing could help, he said.
Dr Baker said higher death rates among Maori and Pacific infants was also concerning.
Between 2003 and 2007, the sudden unexplained death rate for "Maori" and "Pacific" was 2.34 per 1000 infants and 1.31, respectively. It was 0.53 for "other" infants, which included European babies. Women smoking during pregnancy could be a factor, Dr Baker said.