A long time ago, there was a restaurant in New York called Asti, where the waiters sang opera while they served up plates of pasta underneath signed photographs of Babe Ruth and Noel Coward and where, on at least one occasion, Bill Murray led customers – including this writer, who happened to be dining with one of Murray’s friends – in a conga line through the restaurant, out to 12th Street and back in again.

At the Toronto International Film Festival in September, Murray brightened when a visitor reminded him that they’d met before. “Were you there the night we were with what’s-his-name, Sergio Leone?” he says, his voice rising excitedly, “and we tried to stick (him( with the bill?”

Er, no – different table. But the Asti story is just one of hundreds that abound about Murray, who since breaking out on “Saturday Night Live” and becoming a star in such comedies as “Ghostbusters,” “Groundhog Day” and “Caddyshack,” has pursued something of a dual career, cultivating an inscrutably appealing on-screen persona in indie films by the likes of Sofia Coppola, Jim Jarmusch and Wes Anderson, while making himself almost alarmingly accessible off-screen, crashing a group of friends’ kickball game on Roosevelt Island one day and showing up at a college baseball game the next.

The Murray legend, by now, is well known: He doesn’t have an agent, or a manager or a publicist, and takes movie offers only by way of calls to an 800-number that he rarely checks.

It’s precisely this puncturing of movie-star remove, this combination of ubiquity and elusiveness, this refusal to hew to the conventions and tribal rituals of celebrity, that has endeared Murray to his fans over his 35-year career, earning him a store of goodwill that turns out to be crucial to his latest project.

In “Hyde Park on Hudson,” Murray plays Franklin D. Roosevelt, who, like Murray, enjoyed the almost worshipful affection of the American public. In the film, Roosevelt entertains England’s King George VI as the monarch seeks the United States’ support for Britain in its fight against Hitler.

But “Hyde Park on Hudson” also presents a more unsettling portrait of Roosevelt, who, when he’s not secretly tippling with the king, can be seen carrying on an affair with his distant cousin – a relationship that, the film suggests, was just one of many such dalliances in which Roosevelt maintained a balance of disarming sincerity and manipulation.

Murray says he related to what he saw as Roosevelt’s compartmentalization, as well as his shrewd deployment of native charisma.

“When I was doing it, it came from a major highway in here,” he says, pointing to his chest. “Some of that stuff was coming right down the interstate. It was like, whoosh. Because I can do that. I’ve got that weapon, or that tool. I can do that at 90 miles an hour, I can do that at 115.”

For director Roger Michell, the unsavory aspects of story demanded an actor with Murray’s ingratiating brand of charisma.

“The only actor I could see making the film work was Bill,” Michell said at the festival. “Because there’s something forgivable about Bill. There’s something mischievous about Bill. There’s something ineffably charming about Bill.”

If Murray playing Roosevelt feels like natural casting, both physically and psychologically, “Hyde Park on Hudson” represents something of a departure for the actor, who lately has focused on small but toothsome roles in films such as “Get Low” and last summer’s art-house hit “Moonrise Kingdom.”

When he read the “Hyde Park on Hudson” script, he says: “I knew I had to do it. There was something in me at the time saying (that) I had to be more ambitious. Because I don’t really feel like I have any ambition or drive. … I’m not really a hustler, or anything like that.”

But isn’t it that lack of careerism that has worked so well for Murray over the years?

“It has worked for me,” he says. “It’s extremely powerful to say no; it’s really the most powerful thing to say.”