The Tauranga coroner has ruled there is a "high degree of probability" that 2-month-old baby Marcus Te Hira Grey died at the hands of his father.

But police say that despite already investigating the case twice, they do not have enough evidence to charge anyone with the baby's murder.

Marcus Grey died in Tauranga on November 10, 1997. His parents, Marcus Grey sen and Vicki Martin, had taken him to hospital where staff called the police.

The baby had suffered numerous bites, broken ribs and bruises, some of which were about three weeks old.

Grey has since pleaded guilty to wounding his son with intent to injure and is serving a 4 1/2 -year jail term.

In the Tauranga District Court yesterday, coroner Michael Cooney ruled that baby Marcus died from suffocation and said there was a "high degree of probability that the asphyxia occurred as a non-accidental result of the actions" of his father.

Brain and retinal injuries indicated he had been severely shaken.

"In the last three weeks of his short life of eight weeks, Marcus Grey suffered an unacceptable amount of abuse," Mr Cooney said.

Counsel for Marcus Grey, David Bates, questioned Ms Martin about her varied and numerous statements to police about the baby's injuries.

He suggested she may have shaken the baby in frustration or accidentally smothered him as she slept beside him on the morning of his death. Ms Martin denied shaking the baby, but conceded there was a possibility he had suffocated in his sleep.

Mr Cooney made a recommendation to police that the file remain open and that it be continually reviewed.