The girl, who cannot be named for legal reasons, pleaded guilty to manslaughter by diminished responsibility.
Katie was smothered and slashed with a Stanley knife by the teenager on a playing field in Woodthorpe, York, on 9 January. She died later in hospital.
The girl did not speak as she entered her plea via video link at Leeds Crown Court. She denied a separate charge of murder.
Katie’s family were in court to hear the guilty plea.
Nicholas Johnson QC, defending, asked the court if the charge of murder could be put to the girl again and she wrote her plea on a piece of paper.
Her solicitor told the court: “I can confirm she has indicated not guilty to murder but guilty to manslaughter.”
Graham Reeds QC, prosecuting, said: “We are going to accept that plea of manslaughter by diminished responsibility.”
Mr Reeds said the the defendant had developed severe mental health problems during 2016 and had been taken out of school as a result.
He said that she had been self harming since Christmas 2015 and suffering from delusions, believing that people “weren’t human and were robots”.
He said that although psychosis was being investigated prior to the killing, it had not been diagnosed.
However, he said since the killing she had undergone four psychiatric and psychological assessments and there was no dispute that her mental health problems meant she was suffering from diminished responsibility at the time she killed Katie, even though the killing was planned.
He told the court that when the teenager was found in the street in York by a member of the public, she told him Katie was dead and asked where she was.
The man then found Katie lying on a nearby piece of land with a cut to her neck.
A post-mortem examination showed Katie had two severe cuts to her body – one to her neck and the other to her torso – but neither caused her death.
The prosecutor said Katie had been smothered before the cuts were made.
The court heard the teenager handed police a blood-stained Stanley knife which she had taken from her grandmother’s kitchen.
Police also recovered a number of items from the scene and the teenager’s home.
Among the items were drawings of stick-men in various poses depicting killing and death, and a reference to “they are not human”.
The paper was blood-stained and the court heard it had been cut with the same knife used to slash Katie.
Mr Reeds said she had displayed “strange behaviour towards other people and herself”, and had started to self-harm before she killed Katie.
The judge, Mr Justice Soole, said he wanted more questions answering by the medical experts before he could pass sentence. He adjourned the case to 20 July.