Four members of a family who were found dead at a house in West Sussex all died of gunshot wounds, police said.
The bodies of Kelly Fitzgibbons, 40, and Robert Needham, 42, were found with those of their children Ava Needham, four, and two-year-old Lexi Needham.
Police made the discovery in Duffield Lane in Woodmancote near Chichester on the evening of 29 March.
Their family have paid tribute, saying they have been left "devastated and bewildered" by the four deaths.
Sussex Police says it is not looking for anyone else in connection with the deaths.
Ms Fitzgibbons' sister, Emma, said: "Kelly was a wonderful and special person. She was kind, caring, funny and always smiling with an amazing love for life.
"Kelly was a dedicated and loving mother and adored Rob and her two beautiful children. She had many friends and was devoted to her friends and family.
"Kelly will be missed by so many people and has left a hole in our hearts that will never be filled."
Mr Needham's family said: "Robert was a man with a loving, caring young family. He had a beautiful partner Kelly and daughters Ava and Lexi, who he cared for deeply and who cared for him.
"He was a quiet and thoughtful son and brother as well, always there to help when he was needed.
"We are devastated and bewildered at this most difficult of times."
The post-mortem examinations took place on Thursday and Friday and the provisional causes of deaths were recorded as injuries consistent with gunshot wounds.
The inquest into the deaths will open on 8 April.
The body of a pet dog was also found at the house, police said.