Ed Dixon stars as Fat Tony in “Cloak and Dagger,” now playing at Signature Theatre through July 6, 2014. (Margot Schulman)

“That is something I never thought I’d do,” an actor declares in “Cloak and Dagger.” He might want to hold that thought as he reflects in his maturing years on his participation in the creaking antique joke machine of a musical having its world premiere at Signature Theatre.

A wan parody of noirish detective flicks of yore, “Cloak and Dagger” has as its stock in trade uninspired show tunes interrupted by blue quips denoting an age before political correctness. As in: “Sorry I’m late. I was doing a midget in the alley.”

The musical, directed by Eric Schaeffer, revels in B-movie stereotypes of yore. I’m pretty sure Ed Dixon, the composer, lyricist, co-star and book writer of “Cloak and Dagger,” means to send up the caricatures that once were staples of pulpy gumshoe stories. Dixon delivers the “midget” line in one of his many guises in the 90-minute show, that of a hooker in a leopard print who talks like Mae West and looks like Walter Matthau.

Instead of radiating affection, though, “Cloak and Dagger” sends out wave after wave that says: lame. The sight of two veteran actors, Dixon and Christopher Bloch, wearing stringy wigs and fake bosoms and speaking in supposedly comic Asian and Irish accents comes across in 2014 as lazy and desperate.

Unlike such stylish theatrical embraces of the genre as the Larry Gelbart, Cy Coleman and David Zippel musical “City of Angels” or the four-actor stage version of Hitchcock’s “The 39 Steps,” “Cloak and Dagger” aspires to a grade of humor that is the lowest and easiest.

Erin Driscoll and Doug Carpenter are enlisted as Dixon and Bloch’s confederates in the predictably mindless mystery being unfolded, concerning the purloining of a statue called the Golden Venus. Driscoll is the story’s femme fatale, and Carpenter is a dimwit of a private detective. The bland nature of the songs they’re assigned among the show’s dozen numbers — seven of which are reprised — is illustrated by their generic titles: “Doors Close,” “Love Is,” “The Best of Times,” “Love on a Boat.”

Dixon, meanwhile, gives himself a mafioso number that asks the irrelevant questions, “Who put the ‘mob’ in mobster?” and “Who put the ‘hem’ in mayhem?” It’s one of the many unfortunate moments of “Cloak and Dagger” when we know exactly whodunit.

“Cloak and Dagger,” book music and lyrics by Ed Dixon. Directed by Eric Schaeffer. Set, Daniel Conway; costumes, Kathleen Geldard; lighting, Colin K. Bills; sound, Lane Elms; orchestrations, Jordon Ross Weinhold; music direction, Jenny Cartney. About 90 minutes. Tickets, $40-$104. Through July 6 at Signature Theatre, 4200 Campbell Ave., Arlington. Visit www.signature-theatre.org or call 703-573-7328.