Two months before Kaiya was killed her mother was assessed by an experienced psychiatrist as having no symptoms indicative of a serious mental illness.
Twice police used emergency powers in July 2009 and October 2010 to take her from her mother, but Kaiya was returned with "undue haste" the report said.
Manchester City Council said it had had contact with the family before Kaiya's death and a serious case review was to be carried out by the city's safeguarding children board into its involvement.