Terri Harris and her children John Paul and Lacey Bennett were found dead along with Lacey’s friend Connie Gent at a house in Killamarsh on 19 September.
Their inquest openings heard police went to the house following a report Damien Bendall had stabbed himself.
Mr Bendall was arrested on suspicion of murder and has since been charged.
Det Insp Graham Prince told the inquest that Derbyshire Police received a phone call from Dorset Police at 7.26am on 19 September.
“Dorset Police received a telephone call about the safety of Damien Bendall,” Det Insp Prince said.
“That phone call was made by a relative of Damien Bendall. They indicated to Dorset Police that Bendall had suffered a stab wound and that was self-inflicted.”
He said Derbyshire Police were alerted and officers were dispatched to Chandos Crescent in Killamarsh and were met by Bendall when they arrived at 07.39am
Det Insp Prince said police then entered the house “concerned for the safety of the other occupants”.
Once inside the house they located Terri Harris, 35, John Paul Bennett, 13, Lacey Bennett, 11, and Connie Gent, also 11.
They were already deceased, he said, and paramedics confirmed this when they arrived a short time later.
The coroner, Peter Nieto, said post-mortem examinations have been carried out and he is awaiting full reports. However, he said the early indications were that the deaths had been caused by “violent acts”.
He suspended the inquests, explaining that they cannot resume until after criminal proceedings have ended.
Det Insp Prince said Connie had been stopping at the house since 17 September, as she was visiting Lacey and her family.
Mr Bendall, 31, of Chandos Crescent, appeared at Derby Crown Court on Friday morning.
A trial was provisionally set for 1 March.
He is due to appear at the same court for a review hearing on 26 November.