Milliners — all 12 of you still practicing that noble craft — should not get too excited about “Important Hats of the Twentieth Century,” a new comedy by Nick Jones that opened on Monday at City Center in a Manhattan Theater Club production. A parade of historic headgear does not feature in Mr. Jones’s frothy but chiffon-thin play about rivalrous fashion designers, semi-mad scientists and time travel. Mr. Jones’s woolly fantasy, set mostly in 1937, with frequent flights to 1998, begins like a film noir, with a reporter arriving at the scene of a crime. T. B. Doyle, played with funny, square-jawed seriousness by John Behlmann, is interrogating a police officer about a break-in at the laboratory of the “brilliant overweight scientist” Dr. Cromwell (Remy Auberjonois). The cop seems a bit vague about the device purloined and the supposedly grave implications of its theft (“You know these scientists — they think the whole world revolves around science — ha!”), but he’s quite taken with Doyle’s hat, which he finds quite “chic.” We are clearly in fantasyland when beat cops are tossing around lingo like that in 1937.