No alarm bells before Vic baby death

The father of a baby girl killed by her mother in Victoria says he should have been informed of the woman's mental health state before it was too late.

The mother was referred to a psychologist before she killed the girl and seriously injured the baby's twin sister in 2012, but did not go, the Victorian Coroners Court has been told.

The babies' father says he wasn't told about the referral, by his then-wife or any health professionals, and would have sought help for the family if he knew there were problems.

Nothing about the woman's behaviour at time triggered alarm bells, and there had been just one verbal outburst by her, the father said.

"If I witnessed anything we wouldn't be in this situation right now," he said through tears on Wednesday.

"I'm going to be (traumatised) for the rest of my life."

A post-mortem found the injuries to the deceased baby girl's brain, body and ribs were not all inflicted at the same time and were not accidental.

The mother last year pleaded guilty to infanticide - an offence which applies when a mother kills her infant while the balance of her mind is disturbed.

She also pleaded guilty to a count of recklessly causing serious injury relating to injuries sustained by the other twin and was sentenced to a 12 month community corrections order.

An inquest is being held to examine the role of healthcare providers.

The father said he was "shocked and dumbfounded" when, at an appointment two days before the baby girl's death, a nurse asked about bruises and markings on the other twin.

He had never seen them before and couldn't comprehend where they had come from, he told the court.

He said he would have sought immediate help if he was told the marks could be linked to abuse.

The girl's mother had earlier told a maternal child health nurse that the twins bruised their faces after bumping into each other in their cot.

The inquest continues.