The nine-month-old baby and the unnamed 24-year-old woman, who was dependent on insulin, were found at their council flat in Grangemouth, near Falkirk.
A post-mortem examination was being carried out yesterday but police said there appeared to be no suspicious circumstances.
One theory is that the woman died after slipping into a diabetic coma and her baby starved.
The bodies were found by one of the woman's brothers on Saturday night.
Another brother denied claims by neighbours that the bodies had been lying there since December.
Neighbours said yesterday that it was not unusual for the woman to disappear from the flat for weeks at a time.
Relatives of the dead mother and baby last night identified them as Rose McCormack and her son Jack.
Sir Montague Levine, the Southwark coroner, yesterday called for an internal inquiry at St Thomas's Hospital, London, after a 10-month-old boy died nine hours after he had been sent home by a doctor who said that he was well and suggested he drink lots of fluids.Reuse content