Previous incidents involving Jamie Reynolds, who lured and then killed 17-year-old Georgia Williams, are to be investigated after a decision by West Mercia Police.
The force has asked Devon and Cornwall Police to look at its handling of those incidents and find out whether its own investigations "fell short of what is expected".
Reynolds, who was arrested in Glasgow after he was spotted in a car park, is serving a life sentence after admitting murdering former head girl Georgia at his home in Wellington, Shropshire, in May last year.
Mr Justice Alan Wilkie, sentencing the then 23- year-old at Stafford Crown Court in December 2013, told him he "had the potential to progress to become a serial killer".
It emerged in court that Reynolds was handed a police caution in 2008, aged 17, for trying to strangle another teenage girl.
Georgia's father, a serving detective with the West Mercia force, told the judge at the time: "We've been damned by evil to endure this sorrow and misery to the end of our natural lives."