The husband of Epsom College's headteacher had only moved into their home three weeks before allegedly shooting his wife and daughter dead, it is reported.
George Pattison, 39, was found dead alongside Emma, 45, and seven-year-old Lettie at their home in the grounds of Epsom College in Surrey on Sunday.
Police said Mr Pattison legally owned a gun that was discovered at the scene of the tragedy, and confirmed that a homicide probe has been launched.
The deaths are being investigated as a possible murder-suicide.
Neighbours have now suggested that Mr and Mrs Pattison had been living apart in the months leading up to the tragedy, as a sale went through on their former home in Caterham.
They claimed Mr Patterson, a chartered accountant, had been "flitting between that house and the property in Epsom" up until it was sold for a reported £1.5million last month.
One Caterham resident told MailOnline: "I think [Emma] moved out before George.
"The new owners arrived about three weeks or so ago and just before they moved in, a removal firm had taken away the last remaining bits of furniture belonging to Emma and George from the house.
"It was George who handed the keys over to the estate agents. I think he'd been flitting between that house and the property at Epsom."
Mrs Pattison had reportedly contacted her sister with concerns about Mr Pattison in the hours before the killings, and when she arrived at the house she found all three members of the family dead.
While a gun was found at the scene, the force said causes of death will not be confirmed until post-mortem examinations are carried out later this week.
Mr Pattison had been in contact with Surrey Police just days before the killings about his gun licence in order to change his address after the family moved to the school site from Caterham.
A statement from the force said: "We had contact with George on February 2 after he notified us of a previous change of address, as is routine.
"Due to the short period of time between that contact and this incident, we have made a referral to the Independent Office for Police Conduct."
The IOPC said it is assessing the information available to decide if any further action is necessary.
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."
Mr Pattison had held a gun licence for a number of years and it was up for renewal early last year, according to the Times.
Mrs Pattison became Epsom's first female head in September 2022 after six years as headteacher of Croydon High School in south London.
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.
Mrs Pattison's husband George was a chartered accountant who was director of a management consultancy called Tanglewood 2016, according to Companies House.
