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The LAPD has CLOSED its missing persons investigation involving the wife of Scientology leader David Miscavige ... because cops had a face-to-face meeting with her ... TMZ has learned.

The investigation was launched after LAPD detectives received reports that Shelly Miscavige had not been seen publicly in 6 years. As we previously reported, one of the people who contacted cops was actress Leah Remini.

Law enforcement tells TMZ they have determined the missing persons allegation is "unfounded."