Police in Kent say it is "unfair" on the victims of the Chillenden murders to raise questions over the investigation - despite an apparent confession from Levi Bellfield.
The serial killer is now said to have admitted to murdering Lin Russell and her six-year-old daughter Megan in a country lane near Canterbury in 1996.
Michael Stone has been in prison for the past 20 years, having been twice convicted of the crimes.
But today, Assistant Chief Constable for the Kent and Essex Serious Crime Directorate, Nick Downing, said Stone remained convicted - and there was no evidence to support allegations relating to Bellfield.
In a statement, he said: "We feel it is no longer contemporaneous and is unfair on the victims to continue to raise questions or re-release details about the murder investigation and subsequent conviction of Michael Stone.
"Following two trials at which Stone was found guilty by a jury on both occasions, and an appeal to the High Court, Michael Stone remains convicted of the murders of Lin and Megan Russell, and the attempted murder of Josie Russell in 1996.
"The Criminal Case Review Commission re-examined the murder investigation and had access to all forensic evidence, documentation and exhibits from the original investigation, the review by another force, details of the two Crown Court trials and appeals to the High Court.
"Furthermore, Michael Stone made an application to apply for a Judicial Review in respect of his conviction in September 2012. The Honourable Mr Justice Blake ordered that permission for the application should be refused.
"In addition, a comprehensive investigation carried out by the Metropolitan Police Service into allegations Levi Bellfield was involved in crimes for which is he yet to be convicted concluded there is no evidence to support those claims."
Following Bellfield's apparent confession, Stone's legal team has now approached the Criminal Cases Review Commission, which investigates suspected miscarriages of justice.
In a statement, the commission said: "The case of Michael Stone is currently under active investigation at the Criminal Cases Review Commission and we are looking into a number of issues.
"We received the application from Mr Stone’s legal representatives on 23 August 2017. Since then we have taken steps to secure information and materials relating to the investigation and prosecution of the case. It is not appropriate for us to comment in more detail at this stage.
"As is already widely known, the Commission conducted an earlier investigation into Michael Stone’s murder conviction. During that review, which concluded in 2010, we did not identify any basis upon which we could refer the case for appeal.
"In any case where there has been an earlier application to us, we remain ready to give impartial consideration to any fresh application which is based on the possible existence of new evidence or argument in the case."
The Crown Prosecution Service declined to comment on the case.