Certainly, the CIA and FBI knew Oswald and were monitoring him on an occasional basis. A former Marine does not move to Russia, marry a Russian woman and live there for a year without their keeping tabs on the guy.
Oswald had more than one connection with CIA assets: Clay Shaw in New Orleans and George De Morenscheilds (sp?) in Dallas. The CIA also knew he went to the Russian Embassy in Mexico City and had pictures of him there that their people took.
Oswald kills JFK. When the CIA connection is made the CIA knew they would be called on the carpet. That was when the CIA went full out to make sure Oswald was to be charged as a lone gunman. Their invovlment was to protect themselves to avoid any blame.
Of course
To me it has all the earmarks of a classic Mafia “double Hit”. I think officer Tippit was to kill Oswald—but Oswald got wise and shot him first. Jack Ruby was a fall back plan to fix the problem—all on live TV. Ruby knew if he didn’t do it his family would be targeted—so he did the deed (with police help). He knew he had cancer and was going to die. Maybe he, in some sick way, saved the nation.