City first lady Chirlane ­McCray claimed Tuesday she’s not responsible for the day-to-day management of her ThriveNYC mental health initiative, as she ducked repeated questions from lawmakers about its spending and results.

“ThriveNYC was my idea. I’m the founder, I provide the strategic support, I hold meetings on behavioral health and I amplify things to the public,” McCray said at a City Council hearing examining spending and outcomes in the $250 million-a-year program, which launched in November 2015.

“Susan Herman does the day-to-day management and makes the decisions.”

But Herman has been on the job for only two months and told lawmakers, “We are not a new mental health system,” but a program that addresses needs that have gone unmet by traditional services.

That contradicted what Mayor Bill de Blasio said Friday on WNYC radio, where he claimed that “before the Thrive initiative, there was not even a pretense of a mental health system in the city.”

McCray distanced herself from daily management decisions as critics question how Thrive is spending its millions and why it can’t say whether it’s producing positive outcomes.

Throughout the two-hour hearing, McCray and her aides struggled to provide answers.

They didn’t have a tally of how many staffers are working in each of 41 separate programs, how those programs allocate their spending or why some city mental health programs were put under the ThriveNYC banner while others were not.

When repeatedly asked how much of the budget is tailored to programs for treating the seriously mentally ill, McCray tried to dodge and claim that all spending benefits New Yorkers.

“The reason I say that all of Thrive’s budget is tailored to that is because it’s very difficult to say that this is the percentage of our population that is seriously mentally ill,” she said after Councilman Ritchie Torres (D-Bronx) admitted he once sought medical treatment for depression.

“If you,” McCray added — referring to Torres — “didn’t take your depressant every day and you were the victim of violence or something, you could be in that category tomorrow.”

Eventually, the mayor’s budget office provided a figure: Some $30 million of Thrive’s budget is devoted to the seriously mentally ill. The Health Department spends another $270 million, officials said.

At another point, Herman disputed Correction Commissioner Cynthia Brann’s public statements that Thrive has no presence on Rikers Island.

“In early years, what Thrive focused on was implementation and reach — reaching people all over the city,” Herman said, adding the program should get credit for training 700 jailers and providing an art therapy program.