Sgt. Steve Nelson said a man presented a note demanding money to a teller around 12:10 p.m. and fled north through the Plaza Shopping Center parking lot with an undisclosed amount of money.
The suspect did not show a weapon, Nelson said.
The suspect is a white male adult with a goatee-style mustache, approximately 35 years old, 5 feet 8 inches and 180 pounds, Nelson said.
He was wearing a blue plaid button down Pendleton-style jacket with a hood, a dark baseball cap and dark sunglasses.
Anyone with information is asked to call Petaluma police at (707) 778-4372.