Elon Musk’s space venture last year discovered that an employee at one of its contractors falsified product-quality reports for components intended for its rockets, generating concerns at the National Aeronautics and Space Administration, according to federal investigators.

The complaint, filed in federal court on Tuesday, accuses engineer James Smalley with falsifying reports and parts certifications at his former employer, PMI Industries LLC. The Rochester, N.Y.-based company provided precision machining services for parts...