Kent Police said there was an "ongoing investigation into the supply of drugs" in connection with the 25-year-old's death.
She was found by her husband Thomas Cohen with 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, of Kent Police, said recent heroin use "was likely to have played a role" in her death.
A police spokesman said: "Kent Police can confirm an ongoing investigation into the supply of drugs in connection with the death of Peaches Geldof."
Ms Geldof's death marks a parallel to the death of her mother, TV presenter and writer Paula Yates, who died from an accidental heroin overdose, aged 41, in 2000.
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.