Paramedics were called to John "Goldfinger" Palmer's Essex home to reports of a cardiac arrest on 24 June.
But a post-mortem examination on 30 June revealed the 64-year-old convicted conman had been shot in the chest.
Essex Police has referred itself to the Independent Police Complaints Commission (IPCC).
The force said police and paramedics who were called to Palmer's house in Sandpit Lane, South Weald, "initially assessed the death as non-suspicious due to pre-existing injuries due to recent surgery".
"Closer inspection raised doubt and a post-mortem examination was conducted to establish the cause of death," he added.
Earlier, the senior detective in charge of the murder investigation refused to comment on claims the case had been "bungled".
Det Ch Insp Simon Werrett said his priority was to find whoever was responsible and he would not respond to allegations made by a former Metropolitan Police chief that the force had been "utterly incompetent".
John O'Connor told The Sun: "It's one of the most terrible mistakes in policing I've ever heard of."
'The timeshare king'
When asked if the crime scene had been compromised because of the delay in starting the murder investigation, Det Ch Insp Werrett said it was "challenging".
"However, we do have a crime scene and we're deploying our specialist forensic and search officers around that crime scene," he said.
The East of England Ambulance Service, whose crews went to Palmer's house in Sandpit Lane, said his death was not initially raised as suspicious.
Essex Police is appealing for anyone who was in Sandpit Lane on the afternoon of 24 June to come forward.
Palmer was jailed for eight years in 2001 for masterminding a timeshare fraud targeting people across the UK.
He was cleared of handling proceeds from the 1983 Brinks Mat bullion raid at Heathrow Airport, but his alleged involvement earned him the nickname "Goldfinger".
A week-long delay in realising a notorious criminal had been murdered has left police with a "challenging" crime scene, a senior detective said.