This movie I watched was black & white. I think it took place inside some person's house. The one scene I remember was this man turning another character into a voodoo zombie by making him repeat the words "I am dead" and "I am a zombie".
This is King of the Zombies (1941).
King of the Zombies is a 1941 American zombie comedy film directed by Jean Yarbrough and stars Dick Purcell, Joan Woodbury, and Mantan Moreland. The film was produced by Monogram Pictures, and was typical of its B films produced by the Pine-Thomas team. Along with flying scenes, the use of zany characters and slapstick efforts were juxtaposed with a spy and zombie story.
In 1941, a Capelis XC-12 transport aircraft flown by pilot James "Mac" McCarthy (Dick Purcell) flying between Cuba and Puerto Rico runs low on fuel and is blown off course by a storm. McCarthy, unable to pick up any radio transmissions over the Caribbean, hears by a faint radio signal. After crash-landing on a remote island, his passenger Bill Summers (John Archer) and his black manservant/valet, Jefferson Jackson (Mantan Moreland) take refuge in a mansion owned by Dr. Miklos Sangre (Henry Victor) and his wife Alyce (Patricia Stacey).
The quick-witted yet easily frightened manservant soon becomes convinced the mansion is haunted by zombies, and confirms this with some of the doctor's hired help. With the help of Barbara Winslow (Joan Woodbury), the stranded group begins to find out what mysterious events are taking place in the mansion.
Exploring, the group stumbles upon a voodoo ritual in the cellar. It is being conducted by the doctor, who is in reality a foreign spy, trying to acquire war intelligence from a captured US Admiral whose aircraft had crashed in a similar fashion on the island. McCarthy comes under the doctor's spell but Summers comes to his aid. Information is being transmitted to Barbara, but Summers stops the ritual. The interruption causes the zombies to turn on their master. Sangre shoots the pilot but falls into a firepit and dies. With Sangre dead, all the zombies are released from the doctor's spell.
The film features zombies and voodoo rituals, and is set mostly within a mansion on a remote island. There's also a scene where man is being hypnotised, and is asked to repeat the words "I am dead" and "I am a zombie". You can view it at the 47:10 mark in the video below.