"Court Martial" is episode No. 20 of the first season, production No. 15, of the science fiction television series Star Trek. It was written by Don M. Mankiewicz and Steven W. Carabatsos, directed by Marc Daniels, and aired on February 2, 1967.

In the plot, Captain Kirk stands trial on charges of negligence.

During an ion storm, Captain James T. Kirk of the Federation starship USS Enterprise is forced to eject a research pod containing Lieutenant Commander Benjamin Finney to prevent the destruction of the ship; Finney is presumed dead. The damaged ship makes its way to Starbase 11 for repairs. Commodore Stone, commanding Starbase 11, reviews the ship's records and discovers that Kirk ejected the pod while the ship was at Yellow Alert and not Red Alert as Kirk claimed. Because the ship was not yet in serious danger, Kirk is suspected of intentionally killing Finney. Stone further discovers that much earlier in his career, Kirk had served with Finney aboard the USS Republic and had discovered a mistake Finney had made concerning the antimatter system (which, if left unchecked, would have destroyed the Republic had the ship gone to warp drive). Kirk fixed the error and noted it in the ship's log, causing Finney to be given an official reprimand and sent to the bottom of the promotion list. Ever since this time, Finney has harbored a grudge against Kirk, whom he blames for keeping his career at a standstill. Stone asks Kirk to voluntarily step down as captain of the Enterprise, but Kirk disputes the allegations and demands a trial.

Kirk speaks to Lt. Areel Shaw, a Starfleet Judge Advocate General officer and former girlfriend, seeking legal advice. She reluctantly tells him that she has been assigned to prosecute him. Kirk instead obtains legal representation from Samuel T. Cogley, an eccentric but brilliant trial lawyer. At the trial, both Spock and Dr. McCoy speak on Kirk's behalf, while Finney's daughter Jame (who was named after Captain Kirk) watches from the audience. Cogley puts Kirk on the stand, but again, Kirk's testimony contradicts the computer logs, including a visual recording from the bridge security system that clearly shows Kirk ejecting the pod while the ship was on Yellow Alert. During a recess, Kirk comments that Spock may find a better chess opponent in his next captain, giving Spock an idea.

...
Wikipedia