Clay Shaw and the CP Matter

Another mention in Clay Shaw's diary, begun after his arrest, that I never quite untangled, was a reference during the summer of 1967 to the "CP matter." Shaw mentions that he asked Mario Bermudez to check up on it.

There is an FBI document, about 22 pages long, dealing with, among other things, the "CP matter." It is very heavily redacted even today, and a recent request to open it in full was refused; we must wait until the 2017 date set by the Assassination Records Review Board (ARRB) at the earliest.

I have assumed that it has something to do with some rumor related to the Communist Party, but besides that, I am unclear on it, or why Mario Bermudez could specifically have helped in this regard. There are indications that the document still redacted is part of a huge FBI file related to the Burgess, McLean, Kim Philby spy case in Britain. I suspect it deals with some rumors about Shaw during that era, whether substantiated or not.

If anyone has any ideas, all input is appreciated