hite House officials today offered their first explanation of how the written questions and answers were exchanged between the Japanese magazine Shufu no Tomo and Nancy Reagan.

The written questions were given to Mrs. Reagan's chief of staff, Peter McCoy, by former Reagan speechwriter Peter D. Hannaford the day after the Jan. 21 interview of Mrs. Reagan by Japanese journalists, according to officials who did not want to be identified. Hannaford explained that the Japanese interviewers needed additional information to supplement their brief face-to-face meeting with Mrs. Reagan.

Sheila Tate, the First Lady's press secretary, was given the questions by McCoy and prepared the answers. When the answers were ready, McCoy notified Hannaford on Feb. 11 and they were telexed to the Japanese magazine by Hannaford's firm, Potomac International, according to CBS News.

Hannaford purchased Potomac International from White House national security adviser Richard V. Allen just before Reagan's inauguration on Jan. 20. Allen is being investigated by the Justice Department in connection with $1,000 in cash that he was handed by the Japanese interviewers.

Allen has said he intended to give the Treasury the money, offered as a thank-you gift for Mrs. Reagan, but forgot about it until the cash was discovered in a safe eight months later.

Allen denies participating in preparing written answers for the magazine, which sent three women--including Chizaku Takase, the wife of a long-time friend and business associate of Allen--to interview Mrs. Reagan.

Tate earlier had refused to answer questions about the written questions and answers. McCoy was asked last week if Hannaford had telephoned him a few days before the inauguration to confirm the Japanese interviewers' appointment with Mrs. Reagan. He said then that he had no recollection of such a telephone call, but that he would not dispute Hannaford's statement that such a call had taken place.

McCoy made no mention of receiving written questions from Hannaford or of notifying Hannaford that the answers were ready.