Melchett is accompanied by Inspector Slack, "an energetic man who belied his name and who accompanied his bustling manner with a good deal of disregard for the feelings of anyone he did not consider important." Throughout the novel Slack takes the investigation very seriously.
This combination---investigator chummy with the upper classes accompanied by an underling focused only on finding the truth---also occurs in "Gosford Park," Robert Altman's multi-award-winning film from 2001. And, since the name of Colonel Bantry's house in The Body in the Library is "Gossington Hall," this book would seem to be a source for the film.
There are other similarities. People from the film industry turn up as suspects in both, much to the disapproval of the gentry. And in the film, as in the book, the body is found in the library.
There are differences as well, chiefly in the treatment of English social classes. Altman's film startled viewers in 2001 by taking the servants as seriously as the aristocrats. Agatha Christie keeps the servants in their places.
Strictly speaking, Altman was not the first to give servants their due. "Upstairs, Downstairs" a British television series of the 1970s divided its time between upper and lower classes.
And Altman was not the last. More recently, "Downton Abbey" was a transatlantic hit. Watching "Gosford Park," it's hard to miss Maggie Smith in the role of a disapproving dowager if you were a fan of that series. And, if you look carefully in the credits of the film, you'll see a screenwriting credit for Julian Fellowes, creator of "Downton Abbey."