It's hard to believe, but next month when the bust of the Rev. Dr. Martin Luther King Jr. is formally installed in the Rotunda, it will be the first statue of an American black in the Capitol building. One Hill staffer involved in the dedication ceremony said it was an "embarrassing" omission and added that there are no noted American blacks represented in painting or portraiture in the Capitol either, a fact confirmed by the Architect of the Capitol's office. There are a few unidentified blacks represented on wall murals.

Legislation authorizing the ceremony Jan. 16, the day after King's birthday, passed this week. The House-Senate Joint Committee on the Library, chaired by Rep. Frank Annunzio with Sen. Charles McC. Mathias Jr. as vice chairman, approved the placement of the bust. The two will be responsible for the dedication ceremony, which is to bring King's widow Coretta Scott King and other members of the King family there as well as the congressional leadership. Del. Walter Fauntroy, a former King associate, will give the invocation.

The bronze bust by John Wilson of Boston, who was awarded the commission after a national competition, will remain in the Rotunda for one year and then will be moved permanently to the second floor near Statuary Hall. The creation of the King bust was unusual in that it was not requested by his home state (Georgia), King was not an elected political figure and the authorization came about through a congressional mandate championed by former congressman Jonathan Bingham. End Notes

If it were for the biggest mouths on television, Joan Rivers would win hands down. But the Guild of Professional Hairstylists has put her on the Helene Curtis 10 Best Coiffured Women of 1985 list. And as a three-time recipient of the award she makes the Hall of Fame with Nancy Reagan, Barbara Walters, Ann-Margret and Princess Diana. In addition to Rivers, the others making the 1985 list are actresses Susan Lucci, Valerie Bertinelli, Lisa Hartman, Donna Mills, Jamie Lee Curtis, Cybill Shepherd and Shari Belafonte-Harper and singers Pat Benatar and Sheena Easton . . .

On another list, Soviet leader Mikhail Gorbachev and Princess Diana were voted the top newsmakers of 1985. President Reagan's summit meeting with Gorbachev was chosen the top news story of the year by United Press International subscribers. Those findings go along with the heavy speculation that Time magazine will name Gorbachev or Gorbachev and Reagan on their year-end Man of the Year cover . . .

The Phillips Collection may be one of Washington's best kept secrets, but the gallery staff was all atwitter yesterday when actor Rex Harrison showed up there in the morning, and then in the afternoon Capt. Frank Furillo, better known to friends as Daniel J. Travanti, stopped by in the afternoon to view the famous collection . . .

Rep. Jack Brooks was admitted to Bethesda Naval Hospital yesterday for treatment of a bleeding ulcer. The Texas Democrat is listed in excellent condition . . . Actor James Caan was injured yesterday when his car struck a tree on a winding West Los Angeles road. He was taken to UCLA Medical Center and treated for rib injuries . . . Kennedy Center honoree Irene Dunne is resting in Georgetown Hospital and is expected to be released in a couple of days. She is listed in good condition . . .

On the continuing saga of that football jersey of the Chicago Bears' massive William (The Refrigerator) Perry that Sen. Edward Kennedy gave to Speaker Tip O'Neill in celebration of his 73rd birthday: There was a wire photograph of the historic event that even appeared in the Personalities Column this week. Kennedy and O'Neill liked the picture so much that they have both autographed it and sent it on to Perry. Kennedy wrote: "Not exactly Walter Payton and Perry, but not a bad Democratic team either. We could sure use you on first and goal in Congress." O'Neill wrote: "Just about my size with appreciation from a member of the Perry fan club" . . .