Helicopter Safety Act of 2020 This bill directs the Federal Aviation Administration (FAA) to issue regulations to implement National Transportation Safety Board recommendations for crash-resistant systems with respect to existing and new U.S.-registered turbine-powered rotorcraft (e.g., a helicopter) certificated for six or more passenger seats. Specifically, the FAA must require all U.S.-registered turbine-powered rotorcraft certificated for six or more passenger seats to be equipped with a flight data recorder, a cockpit voice recorder, and a terrain awareness and warning system. The FAA may exempt any civilian helicopter from one or more of the equipment requirements.