Jane Meyer, a spokeswoman for the mayor’s office, said that Ms. McCray’s public schedules listed fund-raising calls made on behalf of the fund, but an analysis of those schedules showed just three such calls in the first three years Mr. de Blasio was in office. The pace appeared to pick up last year, with 16 calls on the schedules and seven more in the first two months of this year.

City Hall later provided a list of 44 people contacted by Ms. McCray in 2015 and 2016. Several people on the list, when asked about the call, either did not remember the interaction or did not recall discussing donations.

“She makes calls to share what our priorities are and to get attention and interest from others,” said Mr. Bloch, describing Ms. McCray as a key part of the organization’s fund-raising. He said that she does not typically make direct requests for money, which is a task that he or another staffer will do in follow-up calls.

However, of the 25 one-on-one calls identified on the schedules, in only three cases did the person or the organization they were associated with follow up with a donation, according to a list of contributions provided by the fund.

One exception was Marilyn Simons, a philanthropist married to the hedge fund billionaire James Simons. The couple donated $260,000, earmarked for Ms. McCray’s mental health initiative, in 2015 and 2016. Ms. McCray’s schedules show that last year she made three calls to Ms. Simons, in July, September and December. In December, the Simonses made another donation, of $250,000. A spokeswoman said that they had pledged an additional $250,000, which will be paid this year.

Ms. Simons declined to be interviewed.

But another pattern is revealed by the calls: almost half of those contacted by Ms. McCray were contributors to her husband’s mayoral campaigns (the Simonses each gave the maximum donation to Mr. de Blasio’s re-election campaign last year). In at least two cases, a person made a campaign donation to Mr. de Blasio within days of one of Ms. McCray’s calls on behalf of the fund.