Mission: Impossible - Season 6 Episode 18 : Committed 1973

Syndicate boss Chandler's alibi is provided by Lt. Governor Harrison, who is in Chandler's pocket. Chandler has the husband of the only witness, Nora Dawson, get her committed and proceeds to have her driven insane at a mental hospital he controls. The IMF must get her out and have her testify in 24 hours. Jim gets Casey committed and she is put in a room near Nora, then he manages to get to Nora's cell and she and Casey switch - Jim then takes Nora-as-Casey out. The team get Nora off the island - when Casey-as-Nora is called to testify, she babbles insanely but then removes her mask while the team bring the real Nora in to testify.