It has an impressive set, striking costumes, capable actors, a classic character (Sherlock Holmes) as inspiration, and a script by a playwright with an enviable track record.

Still, if it weren’t for high production values at Meadow Brook Theatre, Ken Ludwig’s “The Game’s Afoot” might easily be mistaken for one of those over-caffeinated, over-hyphenated dinner-theater-comedy-murder-mystery shows. Yes, there’s a murder but the comedy isn’t that funny and the mystery is so mystifying that even after some time to cogitate I couldn’t tell you who committed the foul deed. Not that I would, but, you know.

Dinner-theater-comedy-murder-mysteries are usually harmless fun. The same is true of “The Game’s Afoot,” but you expect more from a play at Meadow Brook: sustained laughs or a comprehensible plot, at least, since they aren’t about to serve you dinner.

The fault here is almost entirely the writer’s. Ludwig (“Lend Me a Tenor,” “Moon Over Buffalo”) knows his way around farce, and “The Game’s Afoot” pokes jovial fun at the comedy-mystery genre with its requisite batch of eccentric characters in a mansion with many doors on a dark and stormy night.

Give Ludwig credit for choosing a real character as his lead character: William Gillette, the American actor and playwright (1853-1937) who found great fame and fortune playing Sherlock Holmes and whose mansion, Gillette Castle, is now a Connecticut state park and the setting of “The Game’s Afoot.”

The play is set on Christmas Eve, 1936. The real Gillette would have been 84, but Ludwig’s is much younger and lives with his mother. Gillette (played by Ron Williams) is recuperating from a gunshot wound to his arm, having been shot while taking a curtain call following one of his Sherlock Holmes performances. He has invited some of his actor friends over to spend Christmas Eve: two couples, Felix and Madge (Andrew Huff and MaryJo Cuppone), and the recently married Simon and Agatha (Jordan Whalen and Vanessa Sawson).

A late arrival is Daria Chase (Cheryl Turski), the most feared theater critic in all New York. Everyone has a motive for wanting her dead (oh, the horror).

That Ludwig has named a character Agatha is no coincidence. “The Game’s Afoot” owes much to Christie’s “The Mousetrap.” That Ludwig did not name any of his characters Noel must be an oversight. There is a séance scene reminiscent of Coward’s “Blithe Spirit” and, in the slyest reference of all, Gillette’s mother (Ruth Crawford) admonishes him, “Don’t be silly, Billy” which echoes Coward’s memorable, “Don’t quibble, Sybil.”

When the police inspector (Julia Glander) shows up (in jodhpurs and tweed jacket and speaking with a British accent even though we’re in Connecticut) and tries to use the telephone, I immediately thought of the classic suspense play “An Inspector Calls.”

This is all homage, not plagiarism, in the service of spoofery, and director Travis W. Walter has his cast in the spirit, speaking in the slightly overdone tones of a 1930s movie. Kristen Gribbin’s set is a high, wide and handsome two-story interior with multiple doors and a hidden room on a turntable. Liz Goodall’s distinctive costumes instantly let us tell one theatrical couple (white jacket, candy-stripe dress) from the other (plaid jacket, bright green dress), and lighting designer Reid G. Johnson provides, among other things, snow falling against a post-twilight sky.

All fun, yes, but you leave the theater feeling a little hungry and it’s not because they didn’t serve you dinner.