Take any genre, any movie in any film series and add Tina Fey to it and the proceedings are always going to be more fun.

Fey joins Kenneth Branagh‘s merry parade of Hercule Poirot period pieces for “A Haunting in Venice,” a spooky, stylish thriller loosely based on Dame Agatha Christie’s novel “Hallowe’en Party.”

Branagh’s ever-so-elegantly romped through these Poirot movies, vamping through murders that must be solved, a mustache and Belgian ACK-sant that must be curled. Now it’s time for someone to make fun of him to his face. The University of Virginia’s wittiest alumna is the perfect woman for the job.

“You’re doing that thing where you pretend to know more than anbody else.”

Fey plays a famous mystery novelist who “borrows” from Poirot’s persona and his cases for her books, a friend — “I ‘ave no friends.” — who is something of an irritant, showing up in Venice after The War, a place of peace and an epicurean life for the now-retired detective, interrupted only by frantic suitors who want Poirot to look into this or that mystery.

That’s why Poirot keeps Portfoglio (the wonderful Riccardo Scamarcio of “The Ruthless”) around, an ex-cop who serves as a bodyguard and personal assistant. But Portfoglio doesn’t keep Fey’s Ariadne Oliver at bay.

There’s a seance coming, a woman who wants to hear from her dead daughter in a supposedly haunted palazzo. Ariadne and Poirot have one thing they can agree on. “Mediums,” spiritualists and psychics are predatory frauds. Let’s go, Poirot, and poke holes in this mysterious Mrs. Reynolds and her “commune with the spirits of the dead” act.

“I am the smartest person I know, and I can’t figure it out,” Ariadne tells Hercule. “So I came to the second.”

Newly-crowned Oscar-winner Michelle Yeoh plays Reynolds with a self-serious gravitas that chills.

“It is the hallow tide (Halloween). We’re close. Your spirit is close…We are listening!”

Kelly Reilly is the mother of the dead woman, who may have killed herself over a love affair. Her “nerve storms” troubled doctor (Jamie Dornan) is present, the doctor’s young son (Jude Hill), along with a Russian who runs the household (Camille Cottin), all sitting in with Poirot, Ariadne, Mrs. Reynolds and her two Roma assistants (Emma Laird and Ali Khan).

Are Mrs. Reynolds and the others hearing from Alicia (via a spirit-typewriter)? Or will Poirot punch out Harry Houdini’s favorite punching bag, “mediums?”

“Terrors for children, Mrs. Reynolds,” Poirot grumbles. “I have been, in life, uncharmed by your kind.'”

A murder will intrude on this All Hallow’s Eve, and everybody’s a suspect. But Poirot is seeing things, and as reluctant as he may be, there may come a point when he has to agree with everybody else present, that there is something supernatural, something relacted to a “children’s curse” associated with this place, in play here. Or not.

“No one shall leave until I find if the living have been killed by the dead!”

Branagh is a stylish old school filmmaker sometimes unjustly criticized for the sort of camera flourishes — he films lots of characters in close-up, camera slightly above peering down on them to increase our unease — that whole schools of cinema worship Welles, Hitchcock and Kurosawa for. Critics have carped on his fondness for adding cinematic sizzle to his pictures since “Dead Again,” his first foray into mystery-thrillers.

Here he uses the beautiful and ancient city sparingly, and a watery palazzo gone to seed makes a splendid set for all these murders and frights and things that go bump in he night.

These Christie films have a shared air of lost affluence, of a more literate, high-toned age of conversation that vanished long before our age of tweets and modern vulgarisms.

“The voices speak,” Mrs. Reynolds intones, explaining her typewriter. “I take dictation.”

Mystery movies these days are harder to pull off as the audience has seen enough of these to often be a step or two ahead of the movie. As in the “Knives Out” pictures, Branagh isn’t constrained by playing by the rules and fear of “cheating.”

But it’s not just the mystery that recommends “Haunting” and its Christie/Branagh antecdents. It’s the world we’re immersed in, the grand casts playing colorful “types” we recognize in it, the forlourn air of this film, of a generation haunted by the second of two world wars which has just concluded.

“Scars are not always of the body,” Poirot knows.

I haven’t loved all of these semi-campy/semi-serious Branagh dates with Dame Agatha. But “Haunting” is an unadulerated delight. Only in “Venice” can you hear Tina Fey scream.

Rating: PG-13 for some strong violence, disturbing images and thematic elements

Cast: Kenneth Branagh, Michelle Yeoh, Tina Fey, Jamie Dornan, Kelly Reilly, Riccardo Scamarcio, Camille Cottin, Emma Laird, Ali Khan and Jude Hill.

Credits: Directed by Kenneth Branagh, scripted by Michael Green, based on the novel by Agatha Christie. A 20th Century release.

Running time: 1:43