As much film and television work as they do individually, Tina Fey and Paul Rudd surprisingly never have worked together. In theory, her smart, zingy persona should mesh beautifully with his easygoing goofiness — or their shared dynamic should bounce, or snap, or have some sort of life to it. Instead, Paul Weitz’s direction of Karen Croner’s script is tonally erratic: too fast in spots and too much of a slog in others.

It certainly doesn’t help that the characters, based on Jean Hanff Korelitz’s novel, feel like types without much nuance. Even reliable comic veterans like Fey and Rudd can’t find much that’s new or fresh in these people, and as a result they have zero chemistry with each other. That’s shocking, I realize.

Fey, as a Princeton University admissions officer, is always uptight, precise and emotionally closed-off. Rudd, as the do-gooder founder of an alternative New England high school, is always free-spirited, adventurous and open-minded. Even in the fantasy world of romantic comedies where opposites attract and sparks fly, these two have no business being together; they never change each other, and that’s supposed to be the source of comedy.

(Note: Spoiler alert in next paragraph.)

You may actually find yourself hoping that they’ll stay apart. (Spoiler alert! They don’t.) Nonetheless, they end up falling for each other in the unlikeliest of scenarios.

Fey’s Portia Nathan has been analyzing and rejecting prospective Princetonians for 16 years now, and as evidenced by her tidy office and the verbatim speech she gives when visiting the nation’s top high schools, she has it down to a science. Ironically, though, she hates children — babies, to be specific — and shares a quiet, safe life with her condescending English professor boyfriend (Michael Sheen, stuck in a one-note, one-joke role).

When the dean of admissions (Wallace Shawn) announces he’s retiring, Portia finds that she and a rival colleague (Gloria Reuben) are the top candidates to replace him. To distinguish herself, Portia agrees to visit the crunchy-granola New Quest school at the urging of its creator, Rudd’s John Pressman, who happens to have been a classmate of hers at Dartmouth.

Turns out, John has a particular student in mind for Portia to meet: the slightly odd but obviously brilliant Jeremiah (Nat Wolff), whom John believes is the child Portia gave up for adoption back when they were in college. (The fact that he remembers so many details from this period so vividly and that he’d track her down to act on them is creepy, but whatever.) And Jeremiah just happens to want to go to Princeton.

At the same time, Portia’s longtime boyfriend unceremoniously walks out on her for another woman (in the kind of scene that only happens in the movies) so now she’s free to be with John, who … isn’t exactly right for her, either.

“Admission” awkwardly grasps for serious feelings within all these wacky deceptions and manipulations and forces heavy, third-act emotions on us that it hasn’t earned. Some of the few moments of heft come courtesy of a radiant Lily Tomlin as Portia’s mother, a maverick feminist and intellectual who has forged her own notion of what it means to be both a woman and a parent, and urges her daughter to do the same. Merely the idea of Tomlin playing Fey’s mom is exciting, but watching these two strong, groundbreaking comedians share the screen is one of the film’s few real joys.

And seeing the college application process behind the scenes — the lobbying, the favors, the weeding-out — is actually kinda fascinating if this is indeed how it all goes down. Given the cynicism that exists in that conference room over those long days of deliberation, as well as some of the more questionable practices that occur, it’s sort of amazing that an actual school would lend its actual name to the film, much a place of Ivy League prestige.

So maybe there were some surprises here after all.

“Admission,” a Focus Features release, is rated PG-13 for language and some sexual material. Running time: 100 minutes. One and a half stars out of four.