Peaches Geldof, 25, daughter of musician and campaigner Bob Geldof, was found dead at her home in Kent on Monday.
Police said at the time that her death was being treated as “non-suspicious but unexplained and sudden”.
The toxicology tests could take “several weeks” to come through, police said on Wednesday.
“Officers continue to investigate the circumstances surrounding the death in order to compile a report for the coroner,” they added in a statement.
Kent County Council has said it will make “a decision on whether there needs to be an inquest” based on the final results of the autopsy.
Officers had been called to the home Peaches Geldof shared with her husband, singer Thomas Cohen, and their two young children following “a report of concern for the welfare of a woman”. Peaches Geldof was pronounced dead at the scene.
The news of her death was met by shock and grief from friends and family.
Peaches Geldof was 11 when her own mother died.
TV presenter Paula Yates died of a drug overdose in September 2000. In September 2012 Peaches Geldof said she had not been able to come to terms with her mother’s death for several years.
Her final tweet on Sunday was a picture of her as a child in her mother’s arms, with the message: “Me and my mum.”
Peaches Geldof’s last column for Mother and Baby magazine was published posthumously on Tuesday.
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