WHAT do we still want from Bill Murray? His unpremeditated film career — in which he has parlayed performances as the happy-go-lucky heroes of 1980s-era slapstick into the existentially uncertain leading men of thoughtful comedies like “Groundhog Day,” “Rushmore” and “Lost in Translation” — would seem to be sufficient. Yet we demand more from this 62-year-old actor, on whose rugged face a playful smirk and a contemplative gaze look equally at home, and he appears happy to give it to us in his life beyond the screen. Tracking his movements in the wild, as he crashes karaoke parties and kickball games, has become an online pastime; Mr. Murray himself has become the folkloric equivalent of a leprechaun or fairy godparent, popping up at unpredictable yet opportune moments.

His latest role, in “Hyde Park on Hudson,” feels true to his resistance to being pinned down in any way. In this film, which is directed by Roger Michell and which Focus Features will release on Dec. 7, he plays President Franklin D. Roosevelt as he manages an affair with a distant cousin (Laura Linney), a visit from George VI of Britain and the crippling effects of his polio. It is a part that almost no one, least of all Mr. Murray, expected him to play, and it once again raises the question: Why does he do what he does?

On a recent visit to New York Mr. Murray gave a journalist a front-row seat to see his carefree philosophy in action. Actually, closer: After Mr. Murray’s interview with another interrogator ran overtime, I was invited to accompany him to an evening appearance at Florence Gould Hall — and onto the stage of its theater, where a private chat turned into a public spectacle for a few hundred members of the Screen Actors Guild. (Imagine accompanying Mr. Murray on a version of the famous tracking shot from “Goodfellas,” through the back rooms and bowels of an unfamiliar building until the moment you expect to part ways and take your seat in the audience, only to realize then that you’re part of the act.)

In these excerpts from that day’s conversations, Mr. Murray spoke about his need for a life free from preconceptions as much as he demonstrated it.