The fifteen-year-old, named by police as Lisa Hutton, was found unconscious at her family home in Strathairlie Avenue, Arbroath, yesterday morning.
Emergency services were called to the house at 10:45am but, despite the best efforts of paramedics, the girl was pronounced dead at the scene.
Detective Chief Inspector Ali Reid of Tayside Police said officers were now carrying out inquiries in the area and a police family liaison officer had been appointed to the girl's family.
He said: "inquiries 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 inquiries."
A report has been made to the Procurator Fiscal and a post mortem examination is expected to take place in the coming days in a bid to try and establish the cause of death.
It is understood there was no evidence of any physical injury, however, and police are looking at "other potential causes".
One resident in the street, who asked not to be named, described the scene in the street. "There are a lot of children and young people live in the street but this morning it was very quiet," they said.
"We saw the ambulance arrive at the house. There were a lot of police and paramedics going in and out, and from the moment they arrived it was obvious it was very serious."
Another neighbour said: "They're nice people. It's a tragedy."
Last night, friends of the girl posted tributes to her on the social networking site Bebo.
One friend wrote on her page: "Lisa Hutton, I'm gonna miss you so much, and I don't know what I'm gonna do without you! I'm never gonna forget you. Rest in Peace best friend."
Others wrote: "I love you Lisa Hutton, so much... RIP gorgeous," and "Words seriously can not describe how much I love you and miss you."
Police refused to speculate on the cause of Miss Hutton's death last night.
Her family were too upset to speak about the tragedy last night.
However, a police source said: "We have a family liaison team with them and they want to be left alone to grieve at what is a terrible time for them."