The Montgomery County school board plans to hire a Los Angeles-based private consulting firm to head its search for a new school superintendent to replace Edward Andrews, who will resign in July after leading the school system through three tumultuous years.

Korn-Ferry International, a nationwide head-hunting firm, has been picked from a pool of six applicants of independent consultants and private firms. Harold V. Webb, the private consultant from Evanston, Ill., who led a similar search for the county school system three years ago before Andrews was appointed, also will be hired as a special consultant, according to school officials.

The selection of the consultants, who are scheduled to sign a contract today, begins the first step in what will be one of the newly elected board's most important decision in its four-year supervision of the 92,000-student school system. Andrews is generally credited with masterfully guiding the old board through a period of controversial school closings and with implementing a more structured approach to academics.

Board members were reticent yesterday when asked about the selection of the consultant, highlighting a desire to set a tone of confidentiality and to avoid the sort of controversy that has plagued Baltimore City's recent search for a superintendent.

An interim superintendent was appointed there last week after a candidate chosen for the job--Gene R. Carter of Norfolk--suddenly rejected the offer and the entire selection process was re-opened. Carter, some school board members charged, turned down the offer after one board member, Milton A. Dugger, called to dissuade him from taking the job.

Montgomery board president Blair Ewing said the Baltimore controversy "did not inspire" the county board's unwillingness to comment on the selection, "but it certainly reinforced it."

Korn-Ferry, which has offices also in Washington and Houston, will be paid $15,000 and traveling expenses to help the new board recruit candidates for the four-year job and narrow down by Jan. 31 what is expected to be a large field of applicants. Once the winnowing is completed, the board is expected to begin interviewing and to eventually invite finalists to the county to meet community leaders.

Korn-Ferry has helped select superintendents in Mamaroneck, N.Y.; Commerce City, Colo., and Dearborn, Mich.

Previous Montgomery boards have had their own controversies over school superintendents. There was a costly nationwide search for nearly a year before Andrews was selected. At the time he was the acting superintendent and said he did not want the job and would not apply.

Ewing, attempting to put to rest speculation that Andrews might again be persuaded to stay on, said yesterday that no one would be considered for the job who did not apply.