Officials for the city’s ThriveNYC program, a mental health initiative, struggled to tell members of the New York City Council during testimony Wednesday how its annual budget of $250 million is spent and exactly how New Yorkers have benefited from the city’s services.

The ThriveNYC initiative, now three years old, is the signature effort of Chirlane McCray, the wife of New York City Mayor Bill de Blasio. In January, Ms. McCray announced that the program would become its own office, which now has 21 employees with a $2 million office budget, according to Susan Herman, appointed to lead the office.

Ms. Herman told members of the council’s Committee on Mental Health, Disabilities and Addiction that ThriveNYC seeks to fill strategic gaps in mental health services and coordinate activities across agencies to share best practices and lessons learned. Core to the work is to “promote the Thrive message”—mental health—as well as raise public awareness and reduce stigma surrounding mental illness, she said.

But how the success of the ThriveNYC is measured—and its overall effectiveness in helping New Yorkers—was an open question during the hearing. Council members said constituent complaints about mentally ill homeless on the subway and on the streets have risen.

Councilman Chaim Deutsch, who represents parts of Brooklyn including Brighton Beach, said he hasn’t seen ThriveNYC public outreach efforts in his district, and he had a difficult time registering for a mental first-aid training, one of the signature efforts of ThriveNYC.