It may or may not be a good career move for Jon Hamm to play a role once associated with Chevy Chase. But that’s what he’s doing in this screwball mystery caper, directed by Greg “Superbad” Mottola, based on the rascally character originally created in a series of novels by author and former Boston Globe reporter Gregory Mcdonald.

Hamm plays Irvin “Fletch” Fletcher, the journalist turned private investigator, a rumpled ladies’ man forever getting into scrapes. The part was taken by Chase in a couple of films in the 80s, although Hamm plays Fletch as a sophisticated wisecrack merchant, without the broad comedy that Chase went for. His Fletch is a fast-talking sleuth who is engaged for a job in Rome by the beautiful and mysterious Italian heiress Angela de Grassi (played by Lorenza Izzo, who was Leonardo DiCaprio’s Italian fiancée in Once Upon a Time in Hollywood).

Her father’s priceless family paintings, including a Picasso, have been stolen; Fletch picks up a lead and heads to Boston, where the missing booty appears to be offered for sale by a weird germophobe art dealer (Kyle MacLachlan). But when Fletch checks into his rented house in the city, he finds a dead girl in the front room and responds with the mild, cynical bemusement that is the keynote of his performance here, and which never changes even when the droll cops Monroe and Griz – nice, deadpan performances from Roy Wood Jr and Ayden Mayeri – suspect that Fletch is the killer. Surely, our lovable rogue Fletch is being framed. But by whom?

It all rattles along with a wacky series of supporting roles for suspects and walk-ons, including Marcia Gay Harden as Angela’s stepmother, and Hamm’s Mad Men compadre John Slattery playing Fletch’s boozy onetime editor, grumbling about journalists all wanting to work from home these days. It’s amiable entertainment, and Hamm may well develop in the character if this becomes a franchise.

• Confess, Fletch is released on 18 November in cinemas.