Cashman's legal team urge the Court of Appeal to order an investigation into what the jury was shown.
The man who killed nine-year-old Olivia Pratt-Korbel has had his latest attempt to appeal against his murder conviction rejected.
Cashman's legal team asked London's Court of Appeal to order an investigation into an allegation that the jury had been given information that was not part of the evidence presented in his trial.John Cooper KC, representing Cashman, had applied for an extension of time to submit an application for leave to appeal his conviction.
Mr Cooper said: "The allegation is of such seriousness that it would be wrong for an investigation not to be ordered. Mr Cooper also told the court there had been suggestions that members of the jury were given panic alarms by police without the knowledge of the defence team.
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