The girl, who is 16 and cannot be named, pleaded guilty to manslaughter by diminished responsibility in July.
Katie was smothered and slashed with a knife by the teenager on a playing field in Woodthorpe, York, on 9 January. She died later in hospital.
Mr Justice Soole at Leeds Crown Court said it was a "truly exceptional case".
'Dangerous risk'
The defendant, who appeared via video link at Leeds Crown Court, sat with her head down clutching a soft toy as Katie's family looked on from the jury box.
The judge told her: "The gravity of the offence of killing a small child speaks for itself. The level of danger to the public is high.
"In the circumstances of your continuing silence, the critical question is whether there is any reliable estimate as to how long that danger will continue."
Her barrister said this was not a "malicious manoeuvre", but a coping mechanism, as she was still suffering from post-traumatic stress.
A previous hearing was told how the girl, who was 15 at the time of the attack, suffered with severe mental health problems and was convinced people "were robots".
She was found standing in a cul-de-sac covered in blood and carrying a Stanley knife as she rang 999 to tell police what she had done.
A post-mortem examination showed Katie had two severe cuts to her body, one to her neck and the other to her torso, but died from being smothered.
In July, after denying murder but admitting manslaughter, the teenager was given a 12-week interim hospital order to allow for further assessment of her mental health before sentencing.
The judge was told the girl began suffering from mental health problems more than a year before the killing and that due to her "irrational beliefs" she may have been trying to prove that Katie was not a robot.
Prosecutors said she had reported delusional thoughts as well as depression, self-harm and suicidal thoughts.
Nicholas Johnson QC, defending, told the previous hearing his client "was clearly crying out for help and support".
During the sentencing hearing, the court was told psychiatrists still cannot agree on the exact nature of the girl's mental disturbance.
Some have explored whether she was suffering from a depressive disorder and others considered if she has an emerging personality disorder.
Mr Johnson explained she had not engaged with the experts and asked the judge to conclude that she was "unwilling because she was unable".
Following sentencing a statement by Katie's family was read outside court by police.
It said: "Our story is about a loving home and family that was torn apart on a day when we lost our daughter.
"Our story goes on into a future where our home feels very empty, but we will keep going for sake of our other children and our grandson.
"Katie's memory will live on in our hearts but also more widely, as a little girl who brought more colour to her world."
Det Ch Insp Andrea Kell, of North Yorkshire Police, said: "This investigation has been one of the most tragic and challenging I have ever dealt with.
"There are no positive results from cases such as these."
No comments: