Star Trek: The Original Series debuted in 1966 when the television censors were still hard at work trying to decide what was too risque to be shown to viewer. It was a time when open-mouthed kisses weren’t allowed, profanity was kept to a bare minimum, with Captain Kirk uttering the one and only curse word in the entire run of the series, and intimate scenes were hinted at rather than shown. And intimacy was one of the issues the network had with Yeoman Rand (played by Grace Lee Whitney) and Captain Kirk as there were constant battles with the network over the exact relationship between the two.
One scene in particular that the powers-that-be chose to delete because it was considered too intimate came from The Corbomite Manuever. After finishing up his physical with Dr. McCoy, a bare-chested Kirk goes back to his quarters to get dressed. Yeoman Rand is already there, apparently, making herself a little more comfortable than the network liked. She hands him a shirt out of his cabinet. Afterwards, he dismisses her. And this was cut from the episode.
Just five episodes prior, though, the network chose to allow the attempted rape of Yeoman Rand by Captain Kirk’s evil side to be shown. Though it had been a bone of contention between the producers and the network, the scene remained in, and it was far more disturbing than seeing a bare-chested Kirk alone in his quarters with Yeoman Rand.
And there were plenty of other “implied” intimacy scenes with Kirk and other women that made it into the series like In the Wink of an Eye when Kirk is putting on his boots in the room alone with Deela. The implication is clear, and she wasn’t even handing him a shirt!