Oh, it’s not as clever as it thinks it is. And truthfully, for a “romp” it only occasionally romps.

But “See How They Run” is still a warm, witty and old fashioned “whodunit” and an equally old-fashioned “theater” comedy, pronounced “THEE-a-turr” in the British style. I found it an old fashioned hoot.

And as a character in the film’s third act complains, “I’m sorry. I’m completely lost. I don’t have a theatrical background,” a little critic-splaining is in order before dashing out to see it (Sept. 16).

“See How They Run” steals its title from an earlier stage hit.

It’s a send up of Agatha Christie’s “The Mousetrap” set early in the London West End run of the longest running play in history — 1953.

“See How They Run” makes note of author Agatha Christie’s proviso that no film of the play be produced while the play was still running, and that she based it on a real life murder.

The film uses actors from that original production as “characters.” Sir Richard Attenborough wasn’t a knight and was never as tall and dashing as actor Harris Dickinson, who plays the “star” of original production of “The Mousetrap.” Diminutive or not, Sir Richard went on to direct “Gandhi” and capped his acting career with a delightful turn as the impresario behind “Jurassic Park.”

As the story is a murder mystery set against a theatrical murder mystery, there’s a Scotland Yard Inspector Stoppard who is on the case and questioning a backstage full of suspects. Tom Stoppard is a great British playwright, and his funniest work was a one-act play that lampooned “Mousetrap” titled “The Real Inspector Hound,” beloved by critics because it’s about critics who get sucked into a stage production they’re ostensibly reviewing.

Knowing this makes the line, “He was a real ‘Hound,’ Inspector” amusing. “See How They Run” has a few inside jokes like this — “Poppycock!” “Hitchcock, actually.” — a sparkling cast and an infectious sense of fun for those with any sort of “theatrical background.”

Hollywood is chomping at the bit to make a film of “The Mousetrap,” and the director hired by John Woolf (Reese Shearsmith) — who really was a producer on “The African Queen” –is a key figure.

Adrien Brody does his best Jack Nicholson as detective J.J Gittes (“Chinatown”) as narrator/director and American cynic Leo Kopernick.

“It’s a whodunit,” Leo growls. “If you’ve seen one, you’ve seen them all.” But “The Limeys? They just eat it up.”

Leo comments on 1950s Britain, which he’s returned to after serving there in The War, and riffs on the tropes of the whodunit genre as the story unfolds.

Somebody’s got to die in the first act, and “It’s always the most unlikable character who gets knocked-off.”

From Christie to “Columbo,” was ever thus. So who gets it? Our narrator, who insults the screenwriter (David Oyelowo), offends the stage actors, irks the producer, and so on down the line.

Enter Police Constable Stalker (Saoirse Ronan), eager to please the disheveled, drunken, limping Detective Inspector Stoppard (Sam Rockwell) who is her reluctant mentor.

With each interrogation, each twist, our breathless Stalker is given to shouting “Case CLOSED!” But the sodden, methodical Inspector isn’t inclined to jump to conclusions.

British TV director Tom George (“This Country”) tries a few tricks to give his picture a prancing pace — split screens to catch reaction shots and chop up a “door slamming” farce sequence. That doesn’t really do the trick. The production design is TV-period piece immaculate — lush sound-staged bars and sitting rooms, vintage cars and posh suits and dresses.

But what works best here is the casting and the acting. Brody’s terrific wisenheimer delivery as Leo in flashbacks — “the last refuge of a moribund imagination,” our pretentious playwright/screenwriter (Oyelowo) calls them — or as narrator, gets the picture on its feet.

The limeys, he delusionally purrs, “go wild for an American accent,” and have ever since The War.

Rockwell and Ronan deliver comically contrasting characters — jaded and tipsy vs. eager and naive.

Oyelowo huffs and puffs and wraps his voice around plenty of “four dollar words,” but Ruth Wilson of “The Affair” is a bit wasted in a small role as the theatrical producer who would do anything to ensure that “the show must go on.”

With Christie undergoing something of a revival thanks to Kenneth Branagh’s Poirot adaptations “Murder on the Orient Express” and “Death on the Nile” and with “Knives Out” setting the bar for new ways to tackle the hoary “Whodunit” formula, what’s not to like about a film that makes the Mistress of Mysteries, Dame Agatha, a character (Shirley Henderson) and her greatest success an object of good-natured ridicule?

The shaky pace and theatrical setting means it won’t be to every taste. But if you think a murder backstage would make a grand scandal (Hitchcock and Christie and Columbo all took shots at this), and that some police commissioner barking that “Fleet Street is all over this like hot jam on a Devonshire scone!” is funny, this might be the movie for you.

Rating: PG-13 (A Sexual Reference|Some Violence/Bloody Images)

Cast: Sam Rockwell, Saoirse Ronan, David Oyelowo, Ruth Wilson, Harris Dickinson, Pippa Bennett-Warner, Shirley Henderson and Adrien Brody.

Credits: Directed by Tom George, scripted by Mark Chappell. A Searchlight release.

Running time: 1:38