Ms. Haspel’s written responses also briefly addressed other important issues that did not come up at her hearing. Asked about the Iran nuclear deal that Mr. Trump withdrew from last week, she said that Iran had continued to substantially meet its commitments. She also said she agreed with the intelligence community’s assessment that Russia interfered in the 2016 election and pledged to “fully cooperate” with the investigations into it, including by the special counsel, Robert S. Mueller III.

But most of the written questions, like those in her hearing, addressed issues related to the C.I.A.’s defunct torture program and her role in it. Several addressed apparent discrepancies in her testimony.

For example, Ms. Haspel had testified that she was briefed about the interrogation program only after a year. But the agency developed its torture techniques in the summer of 2002 and she was running a prison where they were used later that year.

Asked about that disconnect, she wrote that she meant she was told about the program a year after President George W. Bush had signed a then-classified memorandum of notification authorizing the C.I.A. to capture and detain terrorists after the Sept. 11 attacks. The agency considered its interrogation program to derive from that authority.

Ms. Haspel also faced questions about her role in the C.I.A.’s destruction, in 2005, of 92 videotapes of detainee interrogation sessions. As chief of staff to the head of the agency’s Counterterrorism Center, Jose Rodriguez, she drafted an order he issued to destroy the records as congressional scrutiny of the program increased.

During the hearing, she said only one detainee was depicted on those tapes. But declassified documents have indicated that two of the tapes recorded the interrogations of Mr. Nashiri, the detainee tortured in her custody, and the rest were of another prisoner, Abu Zubaydah.

Asked about that apparent discrepancy, Ms. Haspel disclosed that a C.I.A. lawyer who reviewed the tapes in 2002 found that there were no viewable videotapes of the interrogation of Mr. Nashiri, so only one detainee was depicted on them when they were destroyed. (Several of the tapes were blank and two were broken, but it has never been made public which ones; she did not explain how both of the Nashiri tapes were rendered unviewable.)