Officers at Central Police have renewed their appeal for witnesses as they investigate the death of 15-year-old Anna Johnson, a fourth-year pupil at Morrison's Academy in Crieff, Perthshire.
Simon Pengelley, rector at the school, has said the institution is also undertaking its own internal investigation.
Ms Johnson's body was found on Tuesday morning at the foot of a bridge spanning the motorway and linking Stirling with the village of Cambusbarron.
There have been claims on social media the teenager was being bullied, but these have been denied by both the school and her family.
Police say they are following several lines of inquiry and are talking to her friends and classmates, but have not confirmed the allegations of bullying are being investigated.
A spokeswoman for Central Police said: "We do have lines of inquiry we are following, and we are looking into Anna's background and the circumstances connected with her death."
They are looking for anyone near the bridge at the time of Ms Johnson's death, and have narrowed the timeframe they believe the teenager was in the area.
It was initially been reported she was there as early as 6.15am on Tuesday, but officers believe she arrived no earlier than 6.40am, and died around 7am.
Chief Inspector Gordon Dawson said: "We have had an excellent response from motorists and people who were in the area. As a result we are able to narrow the timescales and are keen to hear from anybody who was on the M9 or Birkhill Road bridge in Cambusbarron between 6.40am and 7am on Tuesday, January 22.
"In particular, we want to speak to those driving on the M9 northbound between Junction 9 Bannockburn Interchange, which are the services at Stirling, and Birkhill Road bridge, which is the fourth in a series of bridges before Craigforth at Junction 10."
Ms Johnson's father Paul, a former police constable, said that his family was devastated. He said: "We can't believe she is gone. Some have said this was something to do with the school she went to but it has absolutely nothing to do with this.
"Anna was really happy there – it is an excellent school."
Mr Pengelley described the 15-year-old as a well-respected and popular pupil and urged witnesses to come forward.
He said: "All the staff and pupils at Morrison's Academy are deeply saddened by the untimely death of Anna Johnson. Our thoughts are with her family and friends during this sad time.
"Central Scotland Police are investigating Anna's death and we would encourage anyone who may have witnessed the incident or have any information they may feel be of use to call them.
"The school is committed to supporting the police during their investigation and will be conducting our own internal investigations. Therefore it would be inappropriate of us to provide any further comment at this time.
"Our immediate focus is to provide all the necessary support to Anna's family, our pupils and their parents as well as our staff."
Flowers were left on the bridge yesterday in tribute to the teenager, while tributes also continued to appear on social media.