Unsettled scores and skeleton-free closets litter the stage of the Gerald Schoenfeld Theatre, where Chita Rivera is taking a high-kicking stroll down memory lane in the strenuously innocuous “Chita Rivera: The Dancer’s Life.” Sondheim? Fosse? Robbins? Bernstein? She worked with ’em all. She co-starred with Liza Minnelli twice – once as her mother – watched Elaine Stritch from the wings, and dated Sammy Davis Jr. And with the help of director-choreographer Graciela Daniele, she’s come to Broadway at the age of 72 to tell you … not quite all about it.

Ms. Rivera created roles in a half dozen major Broadway shows and just as many minor ones – “West Side Story” and “Chicago” get a lot more stage time than “Bajour” and “Merlin” – and she appears to have had about three unkind thoughts the entire time. The book, by frequent collaborator Terrence McNally, has nary a harsh word about her ex-husband, the many divas she’s performed alongside, or even the driver of the cab that crushed her left leg in 1986. She coyly admits to disliking a tiny handful of her costars over the last 40 years … and refuses to name names, of course. Sammy Davis was “extraordinary,” Gwen Verdon was “the closest thing I have ever seen to the magic of Charlie Chaplin,” Jerome Robbins “could do anything,” and so on.

She also offers gushing (if admittedly terrified) praise for Ms. Stritch and her talents, which audiences got to judge for themselves in 2002 with “Elaine Stritch at Liberty.” “Chita Rivera: The Dancer’s Life” is in many ways the anti-“At Liberty.” Ms. Stritch had a stool and her black tights; Ms. Rivera has sets (albeit rather flimsy-looking ones) and 10 slinky backup dancers. The writers who gave ideal voice to Ms. Stritch’s caustic philosophy were the droll, world-weary Stephen Sondheim and Noel Coward. And if Ms. Stritch didn’t like the way something went down, she let them – and us – know. Ms. Rivera’s two best friends in the theater world were John Kander and the late Fred Ebb, best known for punchy tunes like “All That Jazz” and “Cabaret.” And she ain’t talking.

Obviously, there’s more to compelling drama than dirty laundry, and a touch of discretion can be refreshing these days. But Ms. Rivera’s internal conflicts presented here are about as rancorous as her external ones: The 18 screws in her leg; losing the role of Anita to Rita Moreno in the “West Side Story” movie; getting divorced; and specializing as a Broadway dancer, with its nagging injuries, instability, low status, and notoriously short shelf life. (With the exception of a one-night benefit, the decade between 1964’s “Bajour” and “Chicago” was totally Chita-less on Broadway.) “That’s how this business is,” she says with a shrug. “Ups and downs.”

The ups in Ms. Rivera’s career were generally connected with her explosive yet deeply disciplined gifts as a dancer, and as anyone who saw her tango with Antonio Banderas in “Nine” two years ago, those gifts remain alarmingly intact. The legs may not get as high as they once did, nor do the notes, but she can still put a song over with panache, and she’s wise to draw heavily from the work of Mr. Kander and Ebb (who collaborated with her on “Chicago,” “Kiss of the Spider Woman,” and three other shows). Their syncopated, salt-of-the-earth belters are tailored perfectly to Ms. Rivera’s strengths, and some of her finest moments come in what amounts to a Kander-and-Ebb medley near the end. By contrast, the new songs by Stephen Flaherty and Lynn Ahrens, who are almost incapable of writing an uninvolving melody, never sound totally comfortable in her mouth.

That medley comes not a moment too soon: The wheels fall off this star vehicle very early in Act II, with three flabby and undistinguished dance sequences. Two of these center on Ms. Rivera’s past beaus and her favorite choreographers; her comments in each are so vague, so toothless, that not even choreographer Graciela Daniele’s constant movement can give the impression that anything is happening during them. And anybody coming into “The Dancer’s Life” knowing nothing about Jack Cole or Peter Gennaro will leave knowing essentially nothing about them, despite Ms. Rivera’s rhapsodic commentary on each. (She does demonstrate a few signature moves from Bob Fosse, the choreographer who least needs this sort of tutorial.)

As well schooled as Ms. Daniele is in the more sedate, integrated choreography common to today’s musicals – audiences need a lot more convincing to interrupt a musical number with a pro tracted dance break these days – she does a fine job tailoring her work to the Golden Age styles that surrounded Ms. Rivera.And she has assembled a talented, hardworking dance corps that fills in the gaps capably without stealing focus from the main attraction.

Mr. McNally’s scripts often walk a tightrope between sentimental uplift and tart zingers; either the diplomatic Ms. Rivera expunged the racy stuff in rehearsals or Mr. McNally saved her the trouble by not writing any. Either way, the resulting verbal warm bath does not show off Mr. McNally’s wry charms particularly well. Equally puzzling is the choice of songs used throughout. “West Side Story” is undoubtedly the primary draw for many, and it’s understandable that Ms. Daniele should allot it a substantial chunk of time. But why stage “Somewhere,” a song Ms. Rivera never performed on stage and isn’t particularly equipped to sing, instead of “America?” She created the role of Velma in “Chicago,” so why do “Nowadays” and not “When Velma Takes the Stand?”

A possible answer to the latter question can be found in the “Nowadays” lyrics. To paraphrase Roxie, Ms. Rivera has clearly liked the life she’s livin’ and lived the life she likes. Her years as a “gypsy” – a jobbing chorus girl moving from one unheralded Broadway role to another – instilled in her an abiding respect and even love for the hoofers still in the trenches.

This allegiance is most obvious in the finale, which offers the biggest difference between “Chita Rivera: The Dancer’s Life” and a show like “Elaine Stritch at Liberty,” for better and for worse. Ms. Stritch ended her piece with a charming anecdote about 8-year-old Brandon de Wilde bursting with enthusiasm backstage at “Member of the Wedding,” and Ms. Rivera also provides a glimpse at the allure of Broadway through a child’s eyes. Only this time the kid’s actually on stage: Ms.Rivera performs one of her most famous duets with a talented but refreshingly unflashy sixth-grader named Liana Ortiz. I would expect to see Ms. Stritch eat a child on stage sooner than share the spotlight with one during her final number. That’s how this business is, at least a lot of the time, and while that sort of ferocity may be jarring to watch, it can make for a hell of a show. Ms. Rivera has assembled what amounts to a choreographed fireside chat. A little fire to go with it would have been nice.

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