The medical examiner's office says provincial law dictates that a thorough investigation be done first into the circumstances of the deaths.
"Once the office of the chief medical examiner has gathered and assessed all relevant information, a decision will be make regarding the course of action that needs to be taken to prevent similar future deaths," a release said Wednesday.
The office said that will take a few months.
Lisa Gibson's two children were found unresponsive in the bathtub of the family's Winnipeg home last week. They were pronounced dead in hospital. Gibson's husband was not home at the time.
The 32-year-old mother's body was found in the Red River a few days later.
Police have said while it may appear Gibson killed her children, they are not ready to rule out other possibilities and are continuing to investigate.
There have been media reports that Gibson sought treatment for postpartum depression after the birth of her son in the spring. A spokeswoman for the Winnipeg Regional Health Authority has said privacy laws prevent the release of any information, but the matter is being reviewed.
An inquest would be run by a provincial court judge and would include sworn testimony from witnesses, including medical experts.
The head of the Canadian Schizophrenia Society has suggested an inquest is needed to find out whether the health-care system handled Gibson appropriately.
"Many in the public would want to know ... did we do everything we could for her?" Chris Summerville said this week.
Manitoba Attorney General Andrew Swan also has the authority to order an inquest. A spokesperson for the minister's office has said that the government's practice is to leave the decision to the chief medical examiner.
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