Ms. Echeverria said initiatives like the proposed expanded mental health care program have the potential to save the lives of officers like her brother, who she suspected suffered from undiagnosed depression and other mental health problems for years.

The son of Cuban immigrants, Officer Echeverria dreamed of carrying a gun and a badge while growing up in West Islip, on Long Island.

After graduating from SUNY College at Brockport in Western New York, he joined the Police Department when he was 31 years old , after several attempts to pass all the necessary exams. He was assigned to the 73rd Precinct in Brooklyn, where he met his future wife, Sheila; they have two children, Robert Jr., 18, and Faith, 11, Ms. Echeverria said.

She recalled that her brother would ramble about unexplained body scratches, bruises and incidents of alleged bullying at work. He once complained that he found a dead rat in his locker early in his career, and that haunted him, she said. Ms. Echeverria said she never knew for sure whether her brother had actually been bullied.

He also confided to her that he had marital problems, job stress and financial struggles, she said.

By early June, Ms. Echeverria said she was so troubled by her brother’s behavior that she reported it to a police supervisor and a department therapist. He was asked to turn in his gun later that month, she said. She later learned the department returned the weapon to her brother a few days later.