The 25-year-old had one leg hanging down to the floor and the other tucked underneath her in a spare bedroom in Wrotham, Kent, on April 7.
At the opening of her inquest in Gravesend, Detective Chief Inspector Paul Fotheringham said recent heroin use "was likely to have played a role" in her death.
It marks a parallel to the death of her mother, television presenter and writer Paula Yates, who died from an accidental heroin overdose at her London home, aged 41, in 2000.
Mr Fotheringham described the unsuccessful efforts Peaches' husband, musician Tom Cohen, made to contact Peaches before he found her body.
Four days before she was discovered, Mr Cohen went with the couple's two sons, Astala, 23 months, and 11-month-old Phaedra, to his parents' London home.
Mr Fotheringham said this was a normal arrangement so he and his wife, a TV presenter and columnist, could concentrate on their work.
Ms Geldof remained at home in Wrotham and in contact with friends and family, appearing to be her normal self.
Mr Fotheringham said the last contact with Ms Geldof is believed to have been at 7.45pm on the Sunday when she had a telephone conversation with a friend.
Chief inspector Fotheringham said Mr Cohen tried to contact his wife the following morning without success.
Mr Cohen then travelled to the family home in Kent with his mother, Sue, and Astala, arriving at about 1.30pm.
"Thomas entered the property and located Peaches in the spare bedroom," said Mr Fotheringham. It was apparent she was dead.
A post-mortem examination was inconclusive.
Further tests confirmed the recent taking of heroin, Mr Fotheringham said. He said: "Recent use of heroin and the levels identified were likely to have played a role in her death."
Mr Hatch adjourned the inquest for a full hearing to take place on July 23.
None of Ms Geldof's family, including her father Bob, were at the hearing, which lasted about 10 minutes.