Heathrow Hub, the originators of the proposal, stated last year that the safety case had been published on their website.
However there is no sign of it there as far as I can see, and a recent announcement from them said that it was only submitted last month to the Airports Commission and the CAA for assessment.
Not that it really matters as the scheme is only shortlisted as a makeweight. It would probably have never have been included at all had the only member of the Airports Commission with actual experience of running an airport not been forced to resign because of a perceived conflict of interest.