It's one of the subtlest scenes in both the book and the movie (and one of the best-acted). What always strikes me about it in both places is that Michael admits he's a fugitive from the law--but Vitelli doesn't think it's a disqualification for Michael to be a suitor to his daughter--a real Sicilian touch. And the novel points out that Vitelli is willing to let Michael visit because he thinks he could be one of those "wild strokes of good fortune that Sicilians believe in" (not the exact words). That scene in both the film and movie had real conviction behind it.