The Queen Anne-style home in San Francisco's exclusive Pacific Heights area had burn marks on the front and garage doors after someone used gasoline to light the fire on Monday evening, police spokesman Albie Esparza said.
"The homeowner smelled smoke and went to the front door and noticed the front door mat was on fire. The homeowner quickly doused the flames and contacted authorities," Esparza said.
The fire, which caused only slight damage, is under investigation by the joint police-fire department arson task force.
"We're looking at a former patient of the doctor who lives at the residence as a person of interest," Esparza said. "There was a previous interaction between the two just prior to the fire. That information was provided to us by the homeowner. We're aggressively pursuing those leads."
The patient's name was not released. No other details about the issue between the patient and doctor were disclosed.
The home is a popular stop for tourists and became the site of a makeshift memorial after Williams committed suicide in August. Hundreds of mourners gathered outside the house, leaving flowers and cards.
It was purchased in 1997 by Dr. Douglas K. Ousterhout, who told NBC Bay Area last summer he was the perfect person to own a house featured in a movie about a man who disguises himself as an elderly female nanny. Ousterhout is a craniofacial surgeon who performs procedures on transgender people.
"I turn boys' faces into girls' faces," he told the local news station in August. "It seemed only natural" to buy the house.
As for the people who flock there, he said, "It's not a problem." (Editing by Cynthia Johnston and Bill Trott)