Emma Pattison, the headteacher of Epsom College – who is believed to have been murdered by her husband – died of shock, haemorrhage and shotgun wounds to the chest and abdomen, an inquest has heard.
Her seven-year-old daughter Lettie, whose full name was Ellette Francesca, died of a shotgun wound to the head, Surrey Coroner’s Court was told.
It is believed George Pattison, 39, murdered his 45-year-old wife and their child, before he took his own life on 5 February.
The family was found dead at their home in the grounds of the private boarding school in Surrey after Mrs Pattison made a distressed call to her sister.
A gun legally registered to Mr Pattison was found at the scene, police said.
After Thursday’s brief hearing, Coroner Simon Wickens said: “I would like to offer my condolences to Emma’s family and friends, and also the wider community she served, and also to the students whose lives she no doubt touched.”
He added: “I would like to offer my sincerest condolences to Ellette’s family and all who have been touched by her life.”
Post-mortem examinations were carried out at East Surrey Hospital four days after the shooting, coroner’s officer Kelly Truss said.
Mrs Pattison’s family have previously said in a statement: “To see the esteem in which Emma is held by all who knew her is an enormous comfort.
“She was everything one could hope for in a daughter, sister, mother, wife, friend, teacher and so much more.
“We are an extremely close family and family was at the centre of Emma and Lettie’s universe. The Epsom College community had become part of that universe for them both.
“Seven-year-old Lettie was Emma’s pride and joy: an adorable, vibrant little girl with a compelling curiosity, a heart-melting smile and an intellect beyond her years.
“The two of them were inseparable, and we take comfort in that they will remain so.”
On Tuesday, the inquest heard Mr Pattison died from a shotgun wound to the head.
A pre-inquest review hearing into the deaths has been set for 27 June.