An autopsy on Peaches Geldof was inconclusive and toxicology tests will be conducted in an attempt to determine what killed the 25-year-old celebrity, police said on April 9.
Geldof was pronounced dead by paramedics at her home in southeast England on April 7.
Kent Police said a post-mortem examination had not revealed the cause and a toxicology report could take several weeks.
Peaches, the daughter of Irish musician Bob Geldof and the late TV presenter Paula Yates, had worked as a model, writer and television presenter.
She grew up in the glare of Britain’s press, which reveled in the late-night antics of her teenage years, and in the shadow of her mother’s death from a drug overdose when Peaches was 11.
More recently she had married for a second time, to musician Tom Cohen, had two young sons and worked as a broadcaster and fashion writer. She said in 2009 that her drug-taking years were behind her.
Police are treating her death as non-suspicious but unexplained. The force said detectives are investigating the circumstances and will hand their report to a coroner, who is likely to hold an inquest.
In Britain, coroners usually hold inquests to determine the facts of unexplained, sudden or violent deaths.