Yes, Hoover had to be involved, since his organization was the most powerful investigative agency in America. It would have been the most powerful in the world if the KJB hadn’t existed.
One only needs to read the Warren Commission’s findings and compare it with the agents on the ground to see the cover-up, with Hoover’s (figurative) fingerprints all over it.
As an aside, I heard that a photo of Hoover performing a sex act with another man was circulated regularly around mob bosses of the time. None of that has to do directly with JFK’s assassination, though.
Only when RFK really began to drive the mob crazy did the order go forth from various contacts in the Mafia and renegade CIA personnel to hit JFK. By removing JFK, RFK would lose his job and LBJ would be able to put things “right” which he did.
RFK knew this was the reason and after the assassination, asked Hoover if this was the reason his brother was murdered. The Warren commission was a “stacked” commission that had various JFK/RFK haters on it, like Allen Dulles. Information coming from those very agencies that were involved was all “scrubbed”.
Throughout the Warren Commission investigation, each agency had to cover their rear ends for reasons of their systematic failures to read the signs of a potential assassination and or prior knowledge about LHO and how the FBI (and others) knew about this (in today's terms) “Person of Interest”. So each agency lied, covered up and deleted a lot of evidence in order to cover their rear ends AND the facts that they (or some of them had)prior knowledge about an assassination attempt.
The cover up was twofold:
1) Cover prior knowledge and or involvement in the assassination of JFK and...
2) Cover up for agency failures, oversights, neglect and mistakes.
That is why, there is a definite cover up. The question is, was the cover up for reason #1 or reason #2 or...both?