The 11-month-old, whose name has been suppressed, died in January 2013 in her mother's Ravenswood unit.

The inquest before coroner Olivia McTaggart began yesterday in the Launceston Magistrates Court.

Counsel assisting the coroner Mick Allen said a post-mortem of the child was consistent with co-sleeping sudden infant death syndrome.

However, other information that surfaced saw the cause of death changed to "undetermined".

Mr Allen said the parents' accounts about the death were inconsistent, ranging from finding the baby unresponsive in the morning to accidentally lying on her during sexual intercourse.

Other evidence suggested that the couple's other disabled child might have lied down on the baby in the bed.

Nothing in the evidence yesterday suggested an intentional death.

The baby's father cried almost entirely throughout the proceedings.

Mr Allen said the parents' relationship was punctuated with family violence, and child protection services were involved with the children.

Two police officers, who gave evidence, said most of the family violence disputes they attended at the home were minor arguments about property or food.

The inquest heard about the mother's frequent cannabis use but an officer who attended the death scene said it did not appear that either parent was affected by drugs at the time.

The inquest is set to put a spotlight on the role of child protection services and sub-contracted organisations, including Mission Australia, in the lead-up to the baby's death.

Police attended the Ravenswood unit for a minor argument less than a week before the death.