The selection of three deputy chairmen of the National endowment for the Arts was announced yesterday by its chairman, Livingston Biddle Jr. He called the appointments "the beginning of a reorganization" of the 12-year-old agency.

They are P. David Searles, now the Endowment's assistant chairman; Mary Ann Tighe, special arts adviser to Vice President Walter Mondale and Joan Mondale, and L. James Edgy jr., executive director of the Ohio Arts Council.

Previously the Endowment has had a single deputy chairman. Biddle was the first, and for the past eight years the deputy to chairman Nancy hanks was Michael Straight.

Biddle attributed the replacement of a single deputy with what he called "a senior management team" to the growth and increased complexity of the Endowment, whose staff has expanded in nine years from about 30 to about 300.

Each of the three jobs pays a salary of $47,500.

Searles, 45, who has been the No. 2 official at the Endowment for the past 18 months, will become deputy chairman for policy and planning. He had been deputy director of the Peace Corps. He will be acting chairman in Biddle's absence.

Tighe, 30, will be deputy chairman for programs, which will give her responsibility for most of the Endowment's arts grants. She said that during her White House days a majority of the letters received about the Endowment have been complaints about the complexities of getting grants. Decomplicating the system, she says, will be her first priority.

Tighe served on the search committee that recommended Biddle to the President as the new chairman.

Edgy, 41, will be deputy chairman for intergovernmental activities. He will coordinate the Endowment's relations with state, regional and local arts councils. In 1966 there were 150 such agencies and now there are an estimated 1,800. Edgy is the immediate past president of the National Assembly of State Arts Agencies.