A man found dead with his private school headteacher wife and seven-year-old daughter legally owned a gun that was discovered at the scene of the tragedy, police said.
George Pattison, aged 39, had been in contact with Surrey Police just days before the killings about his gun licence in order to change his address.
He was found dead with his wife Emma Pattison, 45, and their daughter Lettie at their home in the grounds of Epsom College in Surrey on Sunday.
The Times reported that Mrs Pattison had contacted a close relative with concerns about her husband in the hours before the killings, and when they arrived at the house they found all three members of the family dead.
Surrey Police today confirmed that officers have launched a homicide investigation.
Authorities have not released details of the cause of death but said investigators are confident no one else was involved.
A source told the Telegraph that a member of school staff called emergency services on Sunday after hearing gunshots.
Mrs Pattison became Epsom's first female head in September 2022 after six years as headteacher of Croydon High School in south London.
The force said a firearm licensed to Mr Pattison was recovered from the scene, but cause of death would not be confirmed until post-mortems have been completed later this week.
The force has subsequently made a self-referral to the Independent Office for Police Conduct.
The force added the firing range at the school did not form part of the crime scene and was not a line of inquiry in the investigation.
Detective Chief Inspector Kimball Edey, senior investigating officer on the case, said: "This is an incredibly traumatic incident and we are working around the clock to investigate and understand the exact circumstances which led to this point.
"We understand the public concern and upset, and we will clarify what we can, when we can, while respecting the right to a level of privacy for the families of those who have lost their lives.
"We are cooperating fully with the IOPC in relation to the referral we have made, and we await the outcome of its assessment of what further action may be required.
"Until this has been completed, we will be unable to provide further details on a number of matters."
Boarding students at the college pay more than £42,000 a year and its alumni include Conservative MP Sir Michael Fallon, broadcaster Jeremy Vine and comedian Tim Vine.