When the Tellerite was murdered, I was quite incapacitated.

Proof Sarek was in Epstein's cell!

KIRK: How was he killed?
MCCOY: His neck was broken. By an expert.
KIRK: Explain.
MCCOY: Well, from the nature and location of the break, I'd say the killer knew exactly where to apply pressure to snap the neck instantly.
KIRK: Who aboard would have that knowledge?
SPOCK: Vulcans. On Vulcan, the method is called tal-shaya. It was considered a merciful form of execution in ancient times.
KIRK: Spock. A short time ago, I broke up an argument between Gav and your father.
SPOCK: Indeed, Captain? Interesting.
MCCOY: Interesting? Spock, do you realise that makes your father the most likely suspect?
SPOCK: Vulcans do not approve of violence.
KIRK: You're saying he couldn't have done it?
SPOCK: No, Captain. I'm merely saying it would be illogical to kill without reason.
KIRK: But if he had a reason, could he have done it?
SPOCK: If there were a reason, my father is quite capable of killing. Logically and efficiently.