In August 2018, a service member at a U.S. Air Force base noticed something unusual about a new body camera there: Chinese characters appeared on its built-in screen, including what turned out to be the logo for China’s domestic-security agency.

The discovery, detailed in a criminal complaint unsealed in federal court Thursday, was one clue that led investigators to an alleged scheme by a Long Island company to import surveillance and security equipment from Chinese manufacturers for resale as purportedly American-made goods...