Police Commissioner Michael J. Murphy maintained that women lacked the physical strength and endurance to be sergeants, but the city lost the court battle.

Ms. Shpritzer and Ms. Schimmel passed the test, gained their sergeant’s stripes in 1965, and were both promoted to lieutenant in 1967. Ms. Schimmel became the first woman to be a captain when Mayor John V. Lindsay and Police Commissioner Patrick V. Murphy pinned the bars on her uniform at City Hall on Aug. 26, 1971, the 51st anniversary of the day women won the right to vote.

When Ms. Schimmel retired, she was a deputy chief, a rank she was promoted to in 1978, and commander of the Community Affairs unit. She expressed no regrets, but said she wished she had been able to take part in the kind of police work that had become routine for women.

“I myself never answered a call on the radio and ran up five flights of stairs and called the ambulance,” she said. “When I was starting in the department, women didn’t do that. And by the time they did it, I was already promoted. I’m sorry I missed that, but you can’t have everything, right?”

Born Gertrude Tannenbaum on Dec. 9, 1918, in the Bronx, she was the youngest of three children of immigrants from Austria. Her father, Asher, worked in a clothing factory, then owned a small egg business. Her mother, Ida, died when she was 16, leaving her with household responsibilities. She was an outstanding student at Morris High School and graduated Phi Beta Kappa from Hunter College.

She wanted to become an English teacher, but jobs in the school system were scarce. So she took the police Civil Service test, passed it with ease and joined the department the next year despite her father’s misgivings.

“I thought he was against it because he felt it was dangerous or something like that,” Ms. Schimmel told Greta Walker in the book “Women Today: 10 Profiles” (1975). “Later, he said he was against it because he thought if I liked the career so much, I wouldn’t want to get married.”