The body of the 25-year-old mother-of-two was found at the home she shared with her young family in Wrotham, Kent, on April 7.
At the opening of her inquest in Gravesend, Detective Chief Inspector Paul Fotheringham, of the Kent and Essex Serious Crime Directorate, said a post-mortem examination was inconclusive, prompting further tests.
But he told the hearing: "Recent use of heroin and the levels identified were likely to have played a role in her death."
It marks a parallel to the death of her mother, TV presenter and writer Paula Yates, who died from an accidental heroin overdose at her London home aged 41 in 2000.
Mr Fotheringham spoke of the days and final moments of Geldof - married to musician Tom Cohen - during the brief hearing in front of North West Kent coroner Roger Hatch.
Mr Fotheringham said: "On Thursday April 3, 2014, Thomas Cohen went with his two sons to stay for the weekend at his parents' house in south-east London.
"This is a normal occurrence which enables Peaches and Thomas to complete work in their respective careers."
He added: "It is believed that Peaches spent Saturday afternoon, into the evening, and Sunday morning at her home address alone.
"Throughout this period she maintained telephone contact with family and friends, including contact with Thomas's mother to arrange a family activity, but this was cancelled.
"Peaches maintained contact with family and friends throughout Sunday and at 5pm Thomas's father Keith Cohen took the youngest child, Phaedra, back to Wrotham and spent half an hour with Peaches before leaving the child with her."
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.
He went on: "All of the friends and family who had contact with Peaches during this period described how she seemed her normal self and was making plans for the future, including a family outing for her sons for the following weekend.
"There was no cause for concern."
Mr Cohen tried to contact his wife the following morning without success, Mr Fotheringham added.
He then travelled to the family home in Kent with his mother, Sue, and 23-month-old son Astala, arriving at around 1.30pm.
"Thomas entered the property and located Peaches in the spare bedroom," Mr Fotheringham said. It was apparent that she was dead.
"She was located on the edge of the bed with one leg hanging down to the floor and the other leg tucked underneath her. She was slumped across the bed," Mr Fotheringham said.
Mr Cohen called out to his mother and Phaedra was found in the property, and the emergency services were called.
Police and paramedics arrived and confirmed she was dead. Kent Police started an investigation but the death was "unexplained with no third party" involvement.
A post-mortem examination carried out by Dr Peter Jerreat at Darent Valley Hospital in Dartford was inconclusive.
Further tests confirmed the recent taking of heroin, Mr Fotheringham said.