Richard Tillman is accused of crashing a car into a San Jose post office and igniting "instant fire logs" inside the vehicle on July 20.
He's also accused of spray-painting an outside wall and live-streaming the crime.
Tillman's family has been outspoken about his mental health issues.
He is scheduled for a competency hearing in Santa Clara County next month.
If convicted of malicious destruction of government property, Tillman could face between 5 and 20 years in federal prison and a fine of $250,000.