Could the Soviets publicly try and then later execute those involved in the event the KGB did it alone as a way to demonstrate their innocence? Or hand those over to the US or something?
The Chairman of the KGB himself would have to be arrested, for criminal incompetence, if nothing else. The question is, how high up does the true guilt actually go, and would the Soviets be willing to fork over the guilty parties, despite whatever outside intelligence those people might hagve inside their heads? Soviet "nationalism" being what it was back then, I doubt they would allow any of their citizens to be extradited, no matter how guilty they were.
I think this could get VERY messy in the USSR, as Krushchev himself could well fall from power all the sooner. The thing is, if someone like Brezhnev takes his place, it will be seen as removing the dove in favor of the hawk. Using JFK's assassination to effect Krushchev's removal as well. Meaning the new government in Moscow has GREATER cupability in the crime than Krushchev's!

I wasn't sure if the KGB were caught red handed.
If they are... well that's pretty much it. The American people will be howling for blood. The big question will be how much the Soviets are wiling to give to appease them.
Hence my reference to the abolition of the KGB in favor of a "successor" organization. And a lot of blood flowing, literally, in the Lubyanka.


OTL, when Oswald's strong ties to the USSR and personal support for the Castro Regime was revealed, a veteran long-term undercover FBI/CIA agent was present inside Moscow when Kennedy's assassination took place. Not knowing the agent spoke perfect Russian (his history was that of a long time CPUSA member that the Soviets did not know had been recruited by the FBI years before), the exchange that took place told the agent (Morris Childs) what had happened. It was obvious to Childs that the Soviets were as in the dark as he was, and quite horrified at the possibility that with the assassin having such strong ties to the USSR the USA might go to war over JFK's murder.
After filling Childs in (in English

), he was asked, as an American, by these veteran KGB officers what they should do. "Tell them everything, leave not a single card unturned, even if it means revealing state secrets. Let the Americans come in and do their own investigations as they will, and where ever it may take them." They followed his advice to the letter.
About all the US learned of any consequence was the military information Oswald told the Soviets during his defection interviews (most of it erroneous, as both the Soviets and later the US discovered

). The details of his attemtped suicide went a long way to convincing the US that there was no way ever that the Soviets would trust the biggest loser in the city of Dallas with the assassination of any head of state, nevermind one leading a superpower.