Just double checked my copy of The Star Trek Interview Book. It was episode of The Virginian where the drunken DeForest Kelly let his patient Leonard Nimoy die.
Highly recommend book, BTW. Allen Asherman (author of The Star Trek Compendium) interviews a great many of the cast and crew behind TOS and the movies (up to c. 1988) and reveals a lot of neat tidbits about the production of Trek through the years. Well worth seeking out.