Child abuse investigators are to examine why experts deemed a mother fit enough to look after her daughter days before the girl was killed.
Social services said the mother did not have any mental health issues
Ntsimbi Galtricia, 23, was found lying injured next to her dead two-year-old daughter Trycia Balhous in a flat in Barking, east London, on Tuesday.
Scotland Yard are not looking for anyone else over the girl's death.
Five days earlier mental health experts had decided Ms Galtricia, from the Republic of Congo, posed no risk.
She is in a serious condition in hospital, but her injuries are not thought to be life-threatening, police said.
Police are still trying to trace the father of the girl. He is believed to be in Paris.
Ms Galtricia is understood to have lived in the nine-storey block of flats of Law House on Maybury Road for at least eight months.
She had visited the Community of Congolese Refugees in Great Britain several times over a four-month period earlier this year for advice on how to claim benefits.
Local shopkeepers had barred the mother from their premises because she seemed unstable, shouting and even accusing one worker at a DVD rental shop of being her daughter's father.
She was arrested on suspicion of harassing local people the day before her social services assessment by Barking and Dagenham Council on 9 August, but released without charge.
A council spokeswoman said: "She was found not to have any mental healthcare issues."
Officers from the Scotland Yard's Child Abuse Investigation Command are now investigating the tragedy.
A post-mortem examination on Balthous confirmed she died from a stab wound to the chest, Scotland Yard said on Wednesday night.