"Shore Leave" is a first-season episode of the original science fiction television series, Star Trek. It was first broadcast on December 29, 1966, and repeated on June 8, 1967. It is episode #15, production #17, and was written by science-fiction author Theodore Sturgeon and directed by Robert Sparr. In the episode, the crew of the Enterprise visits a bizarre planet of dangerous illusions.

On stardate 3025.3, the Federation starship USS Enterprise, under the command of Captain James T. Kirk, arrives at a planet in the Omicron Delta system. Scans reveal the planet to be congenial, and the crew is exhausted after three months of continuous operations. Kirk announces shore leave for all off-duty personnel.

But not long after beaming down, the landing parties experience strange occurrences. Chief Medical Officer Dr. McCoy sees a large, anthropomorphic white rabbit hop past hurriedly, and a moment later Alice, from Lewis Carroll's Alice in Wonderland, asks McCoy if a rabbit has passed by. Lt. Sulu finds an antique Colt Police Positive revolver and later is attacked by a katana-wielding samurai. Yeoman Tonia Barrows is accosted and attacked by Don Juan.

Kirk thinks that McCoy's seemingly ludicrous report of seeing characters from Alice in Wonderland is made up only to make him beam down for investigation. Even so, he is convinced by Spock to visit the planet for relaxation. At first, Kirk does not believe the doctor's story, but then he is shown large rabbit tracks as proof. Kirk then stumbles upon young Starfleet Cadet Finnegan, a cocky Irish practical joker and bully who had been the bane of his existence back in his Academy days; and a former girlfriend, Ruth, whom he has not seen in years.

...
Wikipedia