The Crown Prosecution Service is referring the matter to Ofcom.
Police are reporting Channel 4 to the media regulator Ofcom over the way an undercover programme was edited.
The Crown Prosecution Service said the show "completely distorted" what the trio said, a claim Channel 4 rejects.
Kevin Sutcliffe, commissioning editor for Dispatches, said West Midlands police had produced no evidence to support their claims.
He said the one-hour documentary, which was made over a nine-month period and broadcast in January, allowed comment to be seen in a fuller context.
"All the speakers featured in the film were offered a right to reply and none denied making these comments, nor have any of them complained to Ofcom to our knowledge."
Islam, Media, Channel 4, Documentaries, Green Lane Mosque, BBC