Fifteen-year-old Lisa Hutton was found unconscious by her parents at their home in Strathairlie Avenue, Arbroath, this morning.
They called an ambulance but she was pronounced dead at the scene.
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Hide AdA Tayside Police spokesman said the death was not suspicious and that a post-mortem examination is due to take place to try to establish the cause of death.
Detective chief inspector Ali Reid said: "Enquiries are at a very early stage and it is too soon to say what may have been the cause of her death.
"We will await the outcome of medical tests and our own enquiries."