To close out its 2012-13 season, Theatre Baton Rouge has invoked the theme of a Laurel and Hardy movie. They left ’em laughing.

To do so, they went to a reliable source: Ray Cooney, a British playwright renowned for his farces, several of which the local company has produced over the years.

The latest of these is “Move Over, Mrs. Markham,” which opened last weekend. Directed by Kevin Harger, it is a fast-paced festival of double-entendre, physical comedy and seemingly endless complexities that, against all odds, get untangled in the end.

Good farces don’t always get the respect they deserve. Personal theory: Too many playwrights make the mistake of using virtually the entire first act setting up plot-twist dominoes so that the audience can spend the rest of the play enjoying the sight of them falling over. That tends to make for a boring first act.

What makes Cooney’s plays — John Chapman gets co-author credit in this case — so enjoyable is that he cleverly sets up the complications early and gets them started quickly, adding additional situations as the play develops. While “Mrs. Markham” may not be quite as artful as Cooney’s “It Runs in the Family,” which was performed on this stage in 2011, it still is quite good.

Set in 1969 in the London apartment of Joanna and Philip Markham (played by Elizabeth Tadie Canfield and Ronald Coats), it spins a web of deceit from the start. Since the Markhams are going out to dinner, Joanna’s friend and Philip’s boss’ wife, Linda Lodge (Carole Moore) wants to use their apartment for a tryst with Walter Pangbourne (Nicholas Moore). Joanna gets arm-twisted into agreeing. Little does she know that her interior decorator, Alistair Spenlow (Zac Thriffiley), has the same plans with their au pair, Sylvie (Courtney McKay Murphy). Or that Linda’s husband, Henry (Jeffrey Johnson), makes the same plans with a telephone operator, Miss Wilkinson (Michele Taylor).

Naturally, the apartment isn’t big enough for all that. It takes the relationship phrase “It’s complicated” to a quantum level. Identities get mistaken, often intentionally. Sexual preferences get mistaken, quite unintentionally.

Coats gives the strongest performance as the uptight children’s book editor who is appalled by all the sexual libertines in his midst, particularly when he believes that Joanna is one of them. Thriffiley is a close second as the flamboyant decorator with garish, late-’60s tastes that have turned the apartment into a hideous mixture of clashing colors. Both of them are required to be manic for much of the play, and both do manic well.

Canfield also excels as the wife who briefly gets caught up in the craziness, but recovers and keeps her head when all others are losing theirs. The rest of the cast, which includes Lindsey Short as children’s book author Olive Harriet Smythe, is solid.

The play runs 2½ hours and, except for a 15-minute intermission, moves at a fairly breakneck pace. In other words, typical Cooney.