Post-mortem examinations on two toddlers believed killed by their father have proved inconclusive, police said.
Two-year-old Phoebe Case and her sister Nereya, one, were found on Monday morning dead on a bed at their family home in Fordingbridge, Hampshire.
It is believed their father, lorry driver Andrew Case, 33, killed them and stabbed their mother Victoria, 31, before hanging himself.
Reports from neighbours said the children had suffered knife wounds but this has now been ruled out.
Further tests will now be carried out to find the cause of the deaths of the youngsters, who were discovered upstairs in the £250,000 semi-detached property in Provost Street.
The family was reported to have had money problems, with Mr Case repaying cash since 2006 using a formal alternative to bankruptcy known as an Individual Voluntary Arrangement.
Mrs Case, who ran a nearby nursery, is also thought to have owed money on credit cards.
Acting Superintendent Gary Cooper said: "Detectives are still exploring the circumstances that led to this tragic incident and would appeal for anyone who knew the family to contact them with any information that may assist their investigation. They would also like to hear from anyone who had contact with the family, or saw the family, after 2pm on Saturday July 24."
The bodies were discovered by the children's grandmother Linda Haskell, 56, when she called around after being unable to contact the family.
She ran out into the street screaming: "All my babies are dead."