With 25 nominations -- 20 for its own productions, five for shows it has hosted -- Arena Stage dominated the list of candidates for the first annual Helen Hayes Awards, Washington's equivalent of the Tony Awards for excellence in the theater. Arena's closest competitor, the financially strapped New Playwrights' Theatre, received 11.

The nominations, announced yesterday at the British Embassy by Richard L. Coe, critic emeritus of The Washington Post, are divided into two general categories -- resident productions and touring productions.

The most consistently cited shows were Arena's "Cloud Nine," a British comedy about sexual confusions, and New Playwrights' "Lydie Breeze," half of a two-play repertory about an idealistic 19th-century commune coming undone. Each received six nominations in various categories. Arena's marathon "Man and Superman" and the Studio Theatre's "My Sister in This House" gathered five nominations each. All four productions, plus New Playwrights' "The Beautiful Lady," a musical about pre-Revolutionary Russian poets, will contend for Best Resident Production.

Among the touring shows, the Royal Shakespeare Company's production of "Cyrano de Bergerac" led the pack with four nominations, followed by "Cats" and "Torch Song Trilogy," with three nominations each. The three were nominated for Outstanding Touring Production, along with "Foolsfire," "The Gospel at Colonus" and "Quilters."

All told, nominations were announced in 14 categories, including those for acting in lead and supporting roles; set, costume and lighting design; direction; and new play. The winners, who will be presented with abstract medallions, are to be revealed May 13 at the National Theatre in a gala ceremony hosted by actress Helen Hayes.

"The field is outstanding. The full range of nominations reflects the quality, the diversity and the tremendous vitality of professional theater in Washington, D.C.," said Elizabeth Brown, the executive director of the Washington Theatre Awards Society, to representatives of Washington's arts and business communities who gathered early last night for the announcement and later nibbled on quail eggs. The nonprofit Washington Theatre Awards Society was founded 18 months ago to administer the awards, named for the Washington-born actress.

About 100 productions that played in the Washington area from May 1, 1984, to Feb. 28, 1985, were eligible for nominations, which were made by a rotating pool of 44 nominators, drawn from the staffs, boards and audiences of the participating theaters. Seven judges, appointed by the Awards Society, will pick the winners.

In addition to the 14 awards, the Awards Society also announced yesterday the creation of the Sir Thomas Lipton Award for Service to the Washington Professional Theatre Community. The award is named after the founder of the Lipton Tea Co., who in 1930 dubbed Hayes "the first lady of the American Theater," a description that has stuck ever since.

Although the work of 20 local theater groups was considered for nominations, only seven made the list. Besides Arena and New Playwrights', they are the Folger Theatre (seven nominations); Studio Theatre (six), Olney Theatre (six), Horizons Theatre (three) and the Source Theatre (one). In the division for touring shows, the Kennedy Center garnered the most nominations (seven), while the Warner Theatre and the National Theatre shared four each. Dinner theaters were excluded from the first year's judging.

The list of nominations produced the usual assortment of curiosities. While two members of Arena's resident company were nominated for Outstanding Lead Actor in a Resident Production, it was for work they did elsewhere -- Richard Bauer for "Enter a Free Man" at Olney; and Stanley Anderson for "Lydie Breeze" at New Playwrights'. Bauer was also nominated for Outstanding Supporting Actor in a resident production for his performance as the Devil in Arena's "Man and Superman."

Kaye Ballard won a nomination for Outstanding Actress in a Touring Production with her autobiographical one-woman show, "Hey Ma, Kaye Ballard," which closed midway through its six-week run at the Kennedy Center. Sally Struthers was cited for "The Odd Couple," a play that is being substantially rewritten for its Broadway opening in June, while Sal Mistretta of "Cats," nominated for Outstanding Supporting Performer in a Touring Production, was dropped from the cast after the Washington engagement.

Still, the nominations helped lend credence to the notion that Washington has theatrical life and tastes independent of New York. According to Richard Byrant, president of the Awards Society's board of directors, there were 1.4 million paid admissions to 2,600 performances of almost 100 different productions in the 10-month judging period.

This year's judges are: Coe; Charles Mark, editor of the Arts Reporting Service; Kathy Dwyer, program officer, the Eugene and Agnes E. Meyer Foundation; director Fredric Lee; University of Maryland professor Roger Meersman; Nick Olcott, president of the Actors Center; and theater critic Faiga Levine.

Following is a complete list of the nominations:

Outstanding Touring Production: "Cats" (National Theatre), "Cyrano de Bergerac" (Kennedy Center), "Foolsfire" (Arena Stage), "The Gospel at Colonus" (Arena), "Quilters" (Kennedy Center), "Torch Song Trilogy" (Warner Theatre).

Outstanding Lead Actor in a Touring Production: Charles Adler, "Torch Song Trilogy" (Warner); Derek Jacobi, "Cyrano de Bergerac" (Kennedy Center); Percy Mtwa, "Woza, Albert!" (Arena); Mbongeni Ngema, "Woza, Albert!" (Arena); Joe Sears, "Greater Tuna" (Ford's Theatre); James Whitmore, "Will Rogers' U.S.A." (Ford's).

Outstanding Lead Actress in a Touring Production: Kaye Ballard, "Hey Ma, Kaye Ballard" (Kennedy Center); Sinead Cusack, "Cyrano de Bergerac" (Kennedy Center); Diane Frantantoni, "Cats" (National); Lenka Peterson, "Quilters" (Kennedy Center); Sally Struthers, "The Odd Couple" (National).

Outstanding Supporting Performer in a Touring Production: Clarence Fountain, "The Gospel at Colonus" (Arena); Estelle Getty, "Torch Song Trilogy" (Warner); Sal Mistretta, "Cats" (National); Frank Olivier, "Sugar Babies" (Warner); Pete Postlethwaite, "Cyrano de Bergerac" (Kennedy Center).

Best Resident Production: "The Beautiful Lady" (New Playwrights'); "Cloud Nine" (Arena); "Lydie Breeze" (New Playwrights'); "Man and Superman" (Arena); "My Sister in This House" (Studio).

Outstanding Lead Actor in a Resident Production: Stanley Anderson, "Lydie Breeze" (New Playwrights'); Richard Bauer, "Enter a Free Man" (Olney); Kevin Donovan, "Cloud Nine" (Arena); Francois de la Giroday, "Man and Superman" (Arena); Tom Toner, "The Gin Game" (Olney).

Outstanding Lead Actress in a Resident Production: Marcia Gay Harden, "Crimes of the Heart" (Olney); Mikel Lambert, "Much Ado About Nothing" (Folger); Sarah Marshall, "My Sister in This House" (Studio); Mary Ellen Nestor, "Top Girls" (Horizons); Karen Trott, "The Beautiful Lady" (New Playwrights'); Halo Wines, "Cloud Nine" (Arena).

Outstanding Supporting Actor in a Resident Production: Richard Bauer, "Man and Superman" (Arena); Steven Dawn, "Lydie Breeze" (New Playwrights'); Mark Hammer, "Cloud Nine" (Arena); Scott Harlan, "Do Black Patent Leather Shoes Really Reflect Up?" (Olney); Floyd King, "King Lear" (Folger); John Leonard, "The Tempest" (Arena).

Oustanding Supporting Actress in a Resident Production: Brigid Cleary, "Enter a Free Man" (Olney); Peggy Cosgrove, "Crimes of the Heart" (Olney); Elizabeth Duvall, "The Wake of Jamey Foster" (Studio); Barbara Klein, "Top Girls" (Horizons); Tami Tappen, "Lydie Breeze" (New Playwrights').

Outstanding Director of a Resident Production: Dorothy Neumann, "Top Girls" (Horizons); Gary Pearle, "Cloud Nine" (Arena); Elinor Renfield, "Passion Play" (Arena); Elizabeth Swados, "The Beautiful Lady" (New Playwrights'); Douglas C. Wager, "Man and Superman" (Arena); Joy Zinoman, "My Sister in This House" (Studio).

Best New Play: "The Beautiful Lady" (New Playwrights'); "Burial Customs" (New Playwrights'); "The Shady Side" (Source).

Outstanding Costume Design in a Resident Production: Jered Aswegan, "The Tempest" (Arena); Laura Crow, "Cloud Nine" (Arena); Anne Hould-Ward, "King Lear" (Folger); Marjorie Slaiman, "Happy End" (Arena); Marjorie Slaiman, "Man and Superman" (Arena); John Carver Sullivan, "Much Ado About Nothing" (Folger).

Outstanding Lighting Design in a Resident Production: Frances Aronson, "Happy End" (Arena); Frances Aronson, The Tempest" (Arena); Stuart Duke, "King Lear" (Folger); Allen Lee Hughes, "Passion Play" (Arena); Nancy Shertler, "Lydie Breeze" (New Playwrights'); Dan Wagner, "My Sister in This House" (Studio).

Outstanding Set Design in a Resident Production: John Arnone, "Happy End" (Arena); William Barclay, "Much Ado About Nothing" (Folger); Lewis Folden, "Lydie Breeze" (New Playwrights'); Russell Metheny, "King Lear" (Folger); Russell Metheny, "My Sister in This House" (Studio); Loren Sherman, "Passion Play" (Arena).