Nothing nitty gritty here...
Just what do you think would've happened if the Warren investagnation found irrefutable proof that Moscow was directly involved in the assassination of JFK?
"investagnation"? A typo, or an insinuation? A rather clever neologism, if intended.
The PoD is that the USSR would directly sponsor the assassination of a US President, which is highly unlikely, even for the adventurist Khrushchev. And there would be no particular reason to target Kennedy.
But suppose that Khrushchev did go that far off the reservation.
And the US finds out. Hmm. How is it that the Warren Commission finds out, not the CIA or the FBI? Well, let's ignore that.
There are two possibllties: the fact is kept secret, or it is publicized.
If the former - outrage among the US leadership, and a secret ultimatum from the US demanding that the persons involved be removed from power and/or punished. On the Soviet side, general consternation that Khrushchev would do anything like this. Immediate action by the Presidium to remove Khrushchev from power, and quietly liquidate him, with profuse apologies to the US.
If the latter - general outrage, and a public ultimatum from the US demanding the persons involved be surrendered to US justice. I'm not sure how the Soviets would react. There would be consternation, and immediate rejection of Khrushchev, but reluctance to do anything in public that would confirm the US charge or appear as submission to US demands.