The two-time Oscar nominee was spotted waving his arms in the air and muttering to himself. He looked almost as dishevelled as the famous character he played in the 1970s detective programme.
Another passer-by, who refused to be named, said the star looked to be disorientated.
Someone eventually called police, but when officers arrived on the scene Falk convinced them that he didn't need help.
Although he had carved out a successful movie career, Falk became an international star when he appeared in the title role in the long-running TV series Columbo, the famously shabby and apparently absent-minded police detective.
Of course, Columbo in fact possessed a keen mind and invariably solves his cases by paying close attention to tiny inconsistencies in a suspect's story.
He merely puts on a good show of being dim-witted so that the suspects and even his colleagues will be more at ease around him.
Columbo's signature technique is to exit the scene of an interview, only to stop in the doorway to ask a suspect "just one more thing" - often bringing to light the key inconsistency.
The role won Falk four Emmy Awards and a Golden Globe. Four of Columbo's cases gave Falk the chance to work with his longtime friend, Patrick McGoohan, the latter playing the villain of the episodes.
The actor played the detective over a 35-year span, beginning with the film Prescription: Murder in 1968.
He also appeared in a series of serious film roles and even played himself in Wim Wenders cult film Wings Of Desire.
The star is still working and is about to appear alongside Val Kilmer in an off-beat comedy about a heroin addict, entilted Cowslip.
The actor's unusual gaze is caused by a glass eye fitted at the age of three due to a malignant tumor.