The woman died in Maidstone in the early hours of Friday
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A woman who died while her daughter received serious injuries appears to have fallen or jumped from her flat holding the girl, police have said.
The force revealed on Friday afternoon officers had been to the flat in Maidstone earlier but left after deciding there was no risk to the woman or child.
Kent Police said it had voluntarily referred the incident to the Police Complaints Authority (PCA).
The woman was found dead with her badly-hurt daughter, who is believed to be about three-years-old, at Hawley Court in London Road, in the early hours of Friday.
The girl, who had suffered multiple injuries, was taken to hospital in Maidstone.
She has since been transferred to Guy's Hospital in London where she remained in a critical condition in hospital on Friday.
Chief Superintendent Chris Eyre of Kent Police said officers had been called to the scene on Thursday evening after a call from neighbours but left, content there was no danger to the woman and girl.
'Tragic situation'
He said the situation as it stood then had been dealt with by the officers and no action had needed to be taken at that point.
Another call was made by neighbours later reporting noises at the flat.
It appeared the woman was probably dead by the time of the call and no officers were sent to the scene after the call, police have said.
Chief Supt Eyre said Kent Police had voluntarily referred the incident to the PCA so it could rule on whether the force had handled the incident properly.
He said: "We want to ensure there is an independently supervised investigation into the way in which we dealt with this tragic situation.
"In the evening when they spoke to the woman officers concluded that there was no reason at that time to believe there was any risk to her or her child.
"There was a further call from a neighbour who said she had heard noises from the bottom of the flat.
"Police did not send officers to this call.
"It does appear that by the time this call was received the tragedy had already taken place.
"In view of the woman's death we want to ensure there is a full open independent review of the nature and sufficiency of police actions."
A police spokesman said they expected a post-mortem examination on the woman to be carried out on Saturday.