Officer Liu is believed to be the first Chinese-American to be killed in the line of duty in the city. Last year, Officer James Li survived after being shot in the legs on a bus in Brooklyn.

About half of the department’s Asian members are Chinese, reflecting the composition of the city’s overall Asian population. But even with their growth, Asians are still underrepresented in the department relative to the 15 percent of city residents who identify themselves as Asians, census figures show. By comparison, 10 percent of the Los Angeles Police Department’s officers and 13 percent of that city’s population are Asian.

But barriers abounded a generation ago. The department’s 5-foot-8 height requirement for men — overturned by litigation in the 1970s — disqualified an untold number of candidates, especially those who hailed from Hong Kong and southern China, where the men are typically shorter. And few immigrants had law enforcement or military roots; if anything, many, accustomed to repressive governments in China and Taiwan, were suspicious of authority.

Image A member of the Brooklyn Asian Civilian Observation Patrol at a rally last month. Credit... Mike Segar/Reuters

One veteran officer in Chinatown, who moved to New York from Guangdong province when he was 10, said that while his parents were open-minded about his career choice, many of their friends disapproved. He remembered his parents’ friends alluding to a common axiom, which roughly translates as “Good sons don’t become public officials.”

“Few would become cops,” said the officer, who spoke on condition of anonymity because he was not authorized to speak publicly. “But now more and more.”

Other skeptics included the New Yorkers the officers were trying to protect.

“Some people refused to be arrested by me, even when I showed them the badge,” said Thomas N. Ong, who retired in 1999 as a detective and is now a private investigator. “They’d say things like, ‘You’re a cop? There are Chinese cops? I didn’t know Chinese were cops.’ ”