Caitlin Oakley, a spokeswoman for H.H.S., said hiring Dr. Redfield was a rare opportunity to employ one of the world’s leading virologists.

“Dr. Redfield has over 30 years of experience as a groundbreaking scientist, academic researcher and clinician who has been a global leader in the fight against one of the most devastating diseases of our time — H.I.V./AIDS,” Ms. Oakley said.

In Friday’s letter, which was also sent to Senator Lamar Alexander, the Tennessee Republican who is chairman of the Committee on Health, Education, Labor and Pensions, Senator Murray requested a briefing on the subject.

She asked whether the agency made an “extensive and exhaustive” effort to find a director before deciding to pay Dr. Redfield under the special exemption. And she also asked for documentation of those search and recruitment efforts, including the descriptions of the job as a “scientific position.”

Lawrence M. Noble, senior director of the Campaign Legal Center, a nonprofit watchdog, also raised questions about the propriety of invoking Title 42 for Dr. Redfield. The news of his higher salary under the provision was reported earlier by The Associated Press.

“One of the points behind it was that the agency was not able to get these people unless they paid under Title 42,” Mr. Noble said. “It seems somewhat incongruous to have someone who’s been trying to get the job for many years to be paid under it. The C.D.C. has to show that it had to do so to get him, and that it needed him for the job.”

The agencies did not supply the numbers of employees hired under the special statute, when asked about them on Thursday.

A report by the Government Accountability Office in 2012 faulted H.H.S. for its use of the Title 42 program. The report said the agency “does not have reliable data to manage and provide oversight of its use of Title 42.” In over 15 percent of the cases examined, the G.A.O. said it was questionable whether people hired under the program were actually performing scientific tasks. In 80 percent of the cases studied, G.A.O. said that H.H.S. did not show that it had tried to recruit individuals for positions before invoking Title 42 to hire new staff.