Almost as mysteriously as the case appeared, United Technologies Corp. yesterday said its board had cleared Chairman Harry J. Gray of allegations that he tapped the phone and bugged the home and office of former UTC President Robert J. Carlson and another former executive.

Both UTC executives had been considered possible heirs to Gray as head of the giant aerospace and industrial products conglomerate, and both left the company after disputes with Gray. Carlson, the most recent to exit, resigned in September. Gray, it was said, worried about subordinates gaining too much power.

The wiretapping and bugging charges first surfaced publicly in The Wall Street Journal earlier this month. The company said then that a special committee of directors was investigating the charges.

Yesterday, UTC issued a terse statement, saying that "the circumstances surrounding the resignation of Robert Carlson as president have been investigated by the board of directors, and the board reaffirms its confidence in Harry J. Gray, its chairman, the company and its people." Pressed to elaborate, spokesman Tom Drohan read a statement that said, "All of us here are delighted this unfortunate incident is over." He would not comment further.

Neither Carlson nor his lawyer could be reached for comment.

The investigation began after Carlson charged that his home was broken into three times in recent months, possibly by someone placing and then removing bugging equipment. In addition, Carlson is said to have charged that his office at UTC headquarters in Hartford, Conn., was ransacked on his last day as president by someone who may have been trying to remove listening devices. Carlson still sits on the UTC board.

The Federal Bureau of Investigation has said it was conducting a preliminary inquiry into the allegations as a result of the press reports, but the status of that probe could not be determined last night.

The board's investigation reportedly centered on Carlson's charges and on allegations that Gray had also ordered the bugging of Edward J. Hennessy, a former UTC executive and heir apparent who now is chairman of Allied Corp. and considered a bitter rival of Gray's.

Soon after The Journal's bugging story appeared, it ran another story claiming UTC had asked an investment banker to consider a possible bid for Allied. The company first denied interest in Allied, then said Allied had approached it about a merger, which Allied denied.