The baby, identified as Amrita Kaur, was found unconscious with her mother below the first-floor window of their home in the city of Bradford on Tuesday and was taken to hospital where she died from injuries consistent with a fall, a post-mortem examination found.
Her mother, a 36-year-old unnamed woman, has been arrested on suspicion of murder and remains in a critical condition in hospital, West Yorkshire Police said.
A police spokesperson said: "The child who died in an incident at a house in Bradford on Tuesday has been named as Amrita Kaur.
"A 36-year-old woman has been arrested on suspicion of murder. She remains in hospital in a critical condition.
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"Police are not looking for anyone else in connection with the incident, but are asking anyone with information to contact them on 101."
According to local news reports, neighbour Mohammed Yaseen raised the alarm after he was alerted by the woman banging on a bin before he and a local window cleaner tried to help with first aid.
Another neighbour, Masood Rana, described how he witnessed the heartbreaking scene of Amrita being carried out to an ambulance.
Other neighbours said they believed the woman and the child had lived in the house for about three months.