U.S. safety officials are investigating a fatal weekend crash involving a Tesla Inc. vehicle, adding to a series of probes into incidents involving the electric-vehicle maker.

The accident has raised questions both about how the car was operated and the challenges of dealing with a fiery crash.

Local authorities believe the Tesla Model S sedan was operating without anyone in the driver’s seat when it crashed into a tree Saturday night north of Houston, killing the two men inside.

On Monday, Tesla Chief Executive Elon Musk injected additional uncertainty into the situation. Mr. Musk tweeted, “Data logs recovered so far show Autopilot was not enabled.” The car didn’t have the upgraded version of the driver-assistance system that the company calls “full self-driving,” he added.

The National Highway Traffic Safety Administration and the National Transportation Safety Board both said Monday that they were investigating the crash. NHTSA has enforcement authority over auto makers, while the NTSB issues safety recommendations. “We are actively engaged with local law enforcement and Tesla to learn more about the details of the crash and will take appropriate steps when we have more information,” NHTSA said in a written statement.