Jessica Garrett and Paul Diem in the Single Carrot Theatre production of The Flu Season. (Britt Olsen-Ecker)

Will Eno’s melancholy “The Flu Season” poses all kinds of tantalizing questions about love and life, but a new production in Baltimore also makes you wonder: What sort of build-a-theater bug is Charm City catching?

In January 2013, Everyman Theatre moved from its longtime base on Charles Street to a spiffy renovated building near the Hippodrome and the Inner Harbor, and in September the Chesapeake Shakespeare Company will unveil a new stage in the same neighborhood. Now the small and scrappy Single Carrot Theatre has christened its own fetching home down the street from the Baltimore Museum of Art, making a playful intellectual statement by debuting with “Flu Season.”

The performance space is a flexible 99-seat black box with no fixed stage or fixed seating; the Carrots will tailor the high-
ceilinged room to suit each show. (Capacity will typically be 75.) The building used to be a tire shop, but soon it will be dominated by a restaurant and butcher shop run by Spike Gjerde of Woodberry Kitchen, which The Washington Post’s Tom Sietsema recently called “the best restaurant in Baltimore.” The lucky Carrots will share a handsome rustic open door with Parts and Labor, as the restaurant is to be called when it opens in the spring.

“The Flu Season” seems to come from the same impulse as “Drunk Enough to Say I Love You,” the taut political parable by Caryl Churchill that the Carrots puckishly performed just before the 2012 election. Eno’s script is linguistically dizzy, and you could start by describing it as a mash-up of “Our Town” and “One Flew Over the Cuckoo’s Nest.”

It’s in “a sort of hospital,” we are told, and just as “Our Town” has a narrating stage manager, the 2003 “Flu Season” has a character called Prologue to chirpily guide us around. But Eno — a quirky, increasingly popular playwright whose “The Open House” premieres at Manhattan’s Signature Theatre next week, with “The Realistic Joneses” following on Broadway next month — counterweights Prologue with a dry-eyed counterpart called Epilogue.

“Lights! Action!” says Prologue.

“Darkness. Inaction,” Epilogue responds.

Between these two contradictory guides, the audience is escorted through the odd romance between Man and Woman in encounters that play out like wry and angst-y Woody Allen, only far more fragile. Director Alix Fenhagen and set designer Ryan Haase place this fable on a steeply raked stage, guaranteeing that the literal footing will be as tricky as the emotional traction. At times the actors, like anxious groundhogs, pop out of holes cut into the stage floor.

“Is that like something we were hoping someone would say?” Woman asks during one of her cautious conversations with Man.

Jessica Garrett plays Woman, and she has a particular ease with the offbeat rhythms of the script. The sympathy and vulnerability of “Flu Season” is almost entirely concentrated in this character, and in language so witty yet so dry that statements seem to flake away as soon as they’re uttered.

It can be tough to connect consistently with anyone else, although Fenhagen’s cast generally seems to be on the right track. Dustin C.T. Morris’s gentle observations as Prologue are tartly rebutted by Allyson Harkey’s cool and worldly Epilogue, and Paul Diem conveys what seems to be a calculatedly abrasive weirdness as Man.

It’s a slippery play, but the kind of heady challenge that has apparently marked the Carrots during their brief industrious tenure in town. The troupe was officially launched in 2007 by a bunch of recent graduates of the University of Colorado, and dramas such as “Flu Season” — coupled with the company’s bold institutionalizing move — demonstrate a winning eagerness to continue stepping up to the plate.

“The Flu Season,” by Will Eno. Directed by Alix Fenhagen. Lights, Joseph R. Walls; costumes, Heather C. Jackson; sound and original music, Dan Cassin. With Michael Salconi, Genevieve de Mahy and Aaron Henkin. About two hours. Tickets $10-$25. Through Feb. 16 at Single Carrot Theatre, 2600 North Howard St., Baltimore. Call 443-844-9253.