Throughout the 87-minute runtime of the action-comedy “Hot Pursuit,” director Anne Fletcher returns again and again to two gags about her stars’ appearances. In one, Sofia Vergara endures cracks about her age, which one character estimates as 50; in another, Reese Witherspoon is needled about having a mustache. These bits come fast and furious in spite of the fact that Vergara looks a good decade younger than her 42 years, and Witherspoon’s complexion is as clean and hairless as a newborn xoloitzcuintle. While hardly the pic’s worst moments, these feel emblematic of its tendency to look for laughs in all the wrong places, even if it means asking viewers to ignore their own lying eyes in service of a joke. Occasionally so ill calibrated that one isn’t quite sure if its title is even intended as a double entendre, “Hot Pursuit” will have to rely on the drawing power and generally endearing chemistry of its two stars to avoid being outpaced at the box office.

Essentially updating “Midnight Run” for the modern era, “Hot Pursuit” pairs an OCD cop known only as Cooper (Witherspoon) with a pneumatic, materialistic gangster’s moll named Daniella Riva (Vergara), whom the former must somehow safely escort to Dallas so the latter can testify against a drug lord (Joaquin Cosio). With Witherspoon on as a producer, and Vergara credited as an exec producer, the film represents an all-too-rare example of a studio comedy featuring women in charge on both sides of the camera. This alone ought to call for celebration, but it’s hard to cheer too loudly for a film that often misfires with near-Happy Madison levels of imprecision.

For example, the opening credits haven’t even finished before we’re asked to laugh at a hoary sight gag involving a transgender prostitute, as we watch the young Cooper grow up riding along in her dad’s cop car. As an adult, the high-strung Cooper is keen to follow in her father’s footsteps, though she’s been grounded to desk duty after an allegedly hilarious incident in which she impulsively tasered an unarmed teenager and caused his clothes to catch fire. Because if there’s anything more timely in 2015 than trans jokes, it’s police-brutality slapstick.

She’s soon given a chance to atone for her trigger-happiness by helping escort the former Miss Plantain Daniella and her husband to their testimony, though no sooner has she arrived at the Rivas’ sprawling manse than two gangs of gunmen take out her partner and Daniella’s spouse. Escaping with Daniella in a nearby muscle car, Cooper informs her that her husband has been murdered, and her garment-rending wails are played for comedy. (Oh, those hot-blooded Latins and their theatrical reactions to things like loved ones being slaughtered.) Add in a pair of corrupt cops who pin the crime on Cooper, and the chase is on.

A few mildly tone-deaf jokes are hardly enough to sink “Hot Pursuit.” What does, however, is its tendency to belabor the laziest, most obvious gags beyond the point of reason. In a representative early example, Cooper conspires to escape from a duo of assailants by claiming Daniella is “having some issues with lady business of the tampon nature”; this is followed by Daniella giving a lengthy biological description of the process of menstruation; this is subsequently followed by the two fortysomething men grimacing with the sort of shock and disgust rarely seen outside a fifth-grade health class. (This pre-middle-school sensibility extends to the use of phrases like “chestal area” and a Sapphic makeout scene that is remarkably both unfunny and untitillating.)

It’s a shame, because Witherspoon remains one of the more underrated comedic talents of her generation (Elle Woods and Tracy Flick would both be career highlights for most actresses), and she clearly has some fun playing up her character’s mile-a-minute Texan chatter and loping cowgirl gait. Vergara aims for many of the same heavily accented Colombo-Charo notes she hits on “Modern Family,” but without that series’ knowing wit, her character tips into cartoonishness. At times the two give off enough sparks to suggest what they could do in the driver’s seat of a sturdier vehicle, especially with their snappy interrogation of Witherspoon’s love interest (Robert Kazinsky), who literally falls off the back of a truck into the middle of the film. But the script from David Feeney and John Quaintance rarely gives them much to work with.

Fletcher, who directed the watchably mediocre likes of “The Proposal” and “Guilt Trip” with more distinction, handles the pic’s scattered action scenes reasonably well, but the pacing often lags in a weird dead zone between shaggy improv and snappy screwball, without nailing the freedom of the former or the fizz of the latter. Louisiana stands in for Texas well enough, and tech work is pro.