The Military Reaction Force was the subject of a Panorama programme.
Former members said the unit had shot people who may have been unarmed.
Last month families of people allegedly killed by the unit said they had been told former members who appeared on the programme had admitted no crimes.
However, in a statement on Tuesday, the police said: "The allegations of serious crime made against the MRF and the contents of the Panorama documentary are under investigation.
"Police have informed the PPS (Public Prosecution Service) of the proposed next steps and the Policing Board were briefed on Thursday 5 June."
Police have said they are investigating allegations against members of an undercover Army unit featured in a BBC documentary last November.