Fast-paced, but only intermittently funny, Carpenter Square Theatre’s production of “Tom, Dick and Harry” has a laughs-to-jokes ratio that is positively woeful. Proof positive that rapid-fire gags don’t necessarily equal rapid-fire chuckles, this screwball comedy could use some more time back on the old drawing board.

Tom Kerwood (Terry Veal) and his wife, Linda (Dawn Deckman Moeller), are looking to adopt a baby, and a visit from the adoption agency representative, Mrs. Potter (Too Too Cirlot), is all that stands between them and parental bliss.

Their home in the Kennington suburb of London is perfectly in order, and they have the child safety information memorized backwards and forwards. But the meticulously rehearsed production is under threat from Tom’s ne’er-do-well brothers, Dick (Christopher Curtis) and Harry (Brett Young).

The pair can always be counted on for a crazy scheme, and they don’t disappoint expectations. Dick has just smuggled hundreds of thousands of cigarettes into the country from France, and Harry has a sack of cadaver parts meant to drive down the value of Tom and Linda’s rented house to make it easier for them to purchase.

Things fall apart almost instantly though, and matters are compounded by a pair of Albanian refugees (Caitlin Cairns, Paul Smith), who snuck in with the cigarettes, and a curious constable (Ryan Joseph Swartz) who’s always poking his head in at the most inconvenient times.

By the time Mrs. Potter arrives, the harried Tom has concocted an ever-growing series of lies in an attempt to maintain the appearance of normalcy. Failure ensues.

Structurally, “Tom, Dick and Harry” has all the elements of a rowdy and riotous farce, but the humor rarely supersedes a tepid level. It doesn’t help that the show depends on a host of terrible British accents that sound as if they were merely an afterthought. Chief offender is Veal, who starts out unconvincingly and only becomes more inconsistent as his histrionics mount.

The absurdity is nearly devoid of surprises and is so repetitive, it becomes tiresome before intermission hits (Tom tells his brothers to leave, brothers do something crazy, Tom lies to cover it up, repeat, repeat, repeat.)

Elsewhere, blunt attempts at wordplay (double entendres on “pussy” and “fags”) and fish-out-of-water humor (foreigners are funny because they don’t understand English!) similarly score low on the laugh meter.

Fortunately, Curtis’s carefree charm as Dick and Young’s gangly physical humor as Harry ensure the show doesn’t pass without at least a small dose of laughs.

Set design by Caleb Schnackenberg and Rhonda Clark effectively creates the feel of a quaint British suburban home, and it uses all of the available space nicely. Costume design by Charlotte Rose is low-key, but appropriate.