In November 1963, 17-year-old Laura Welch ran a stop sign and crashed into another car, killing its teenage driver. Such accidents don’t usually end up on the animated series “Family Guy,” but that one did — because Laura Welch went on to marry George W. Bush and become first lady of the United States.

Now the cartoon’s joke serves as title and throughline for the sneakily engaging solo play “Laura Bush Killed a Guy,” at the Flea Theater.

Ian Allen’s comedy is divided into three short sections, each one starting with Mrs. Bush (a nicely understated Lisa Hodsoll) lamenting the fact that judging by Google searches, her claims to fame are her Cowboy Cookies recipe and that fateful night in Texas. (For the sake of critical thoroughness, I helped myself to one of the free treats at the theater; it was tasty, even if the coconut-cowboy connection remains murky.)

The first go-round makes clear that this will not be a standard bio-play, as Mrs. Bush breezily explains that the accident was, in fact, a cover-up for a deliberate murder. Opening the second part, she contends she had been drunk; the third time is a matter-of-fact account of a driving mistake with tragic consequences.