That is exactly the sort of thing risked by anyone seeing “Broken Nails: A Marlene Dietrich Dialogue,” especially at the front tables of La MaMa E.T.C.’s upstairs cafe-theater. “Broken Nails,” presented by La MaMa with the Polish Cultural Institute of New York, is a slyly fascinating one-woman show (two-woman, if you count the puppet) performed skillfully and with a haunting mix of wit and gravity by Anna Skubik, an award-winning Polish puppeteer and actress.

This is a bare-bones production, yet it’s glamorous. The set consists only of an old trunk, which opens to reveal beautiful costumes on hangers, a dressing table, a lighted makeup mirror and a bentwood chair. The Dietrich puppet is a no-frills model, but she’s dressed in a slinky gold brocade gown — just the sort of thing the real Dietrich might have worn in her nightclub appearances.

Dietrich died in Paris in 1992 at 90. “Broken Nails” takes place at some point during those last years and revolves around Dietrich and her maid, Gloria, who have become weirdly co-dependent. The relationship seems largely hostile. Marlene, whom Gloria always calls “madame,” probably envies her employee’s youth and beauty. But it’s a good thing that Gloria is there because, as Marlene complains, “everyone left me years ago.” There is also a suggestion of sexual desire between the women.

Romuald Wicza-Pokojski wrote and directed “Broken Nails.” But Ms. Skubik created the show, along with Mr. Wicza-Pokojski’s Wiczy Teatr in Torun, Poland. And with Barbara Poczwardowska she designed the puppet, a memorable and terribly sad creation, especially when it sings or says things like, “Fame is such a little word.” It is also the first puppet that I have ever seen getting a massage.