Both actresses that played Nurse Chapel and Uhura were sleeping with the boss Gene Roddenberry.
Gene Coon who did much of the writing and directing once walked into Roddenberry’s office to talk to him about something and while they were talking in comes Uhura from the next room wearing just a shirt that belong to Roddenberry....
From what I have read on Roddenberry he was quite the user of drugs which caused the studio to sidetrack him from the future Star Trek movies as he became erratic.
He was a notorious womanizer.