Bassey claimed the youngster could not have taken her own life after her body was found floating in a river in England in 1985 - because she suffered no "broken bones" and there was no "water in her lungs".
Detectives looked into new allegations made by Penny Beale, whose daughter, also Penny, was battered to death in 2001 by her partner Michael Moffat.
Beale claimed Moffat, who was sentenced to 11 years behind bars for the crime, had admitted to killing Bassey's daughter.
But Detective Inspector Ed Heath insists the investigation has failed, explaining, "All lines of inquiry have been followed. This concluded that there is no evidence of any criminal act involved."