After a preelection truce, National Labor Relations Board chairman Donald L. Dotson and two other members are squabbling again, this time in a barrage of finger-pointing letters sent to a congressional subcommittee.

The White House had told the independent board before this month's election that it wanted to squelch a well-publicized and frequently bitter feud between Dotson and Patricia Diaz Dennis, a Democrat appointed by President Reagan, and Don A. Zimmerman, an independent appointed by President Jimmy Carter.

The warning contained a thinly veiled threat that if Dotson did not patch up relations with Dennis, one of the Reagan administration's highest-ranking Hispanic women, he could be stripped of his chairmanship.

The latest spat was sparked by a letter Dotson sent to the House Government Operations subcommittee on manpower and housing after it issued a report in October criticizing the board for its huge backlog of cases.

Dotson said the subcommittee had failed to consider all the reasons for the logjam.

New board members must "undergo a shakedown period," Dotson said, during which they familiarize themselves with cases. "The result is that the first three to eight months of the appointee's decision-making is likely to be somewhat tentative and to have adverse effects on the board's productivity," he said. "Similar, though slightly different considerations apply at the end of a board member's term" when a departing member is disengaging from cases, Dotson said.

Dotson also said in the letter, which was released to the press, that neither he nor Robert Hunter, a Republican board member also appointed by Reagan, "have had any difficulty over the last year maintaining a high level of productivity . . . . "

Dennis, who is the newest member of the board, and Zimmerman, whose term ends next month, saw Dotson's letter as an attempt to blame them for the backlog.

"We had not planned to respond, but Chairman Dotson's response compels us, reluctantly, to do so," Dennis's chief counsel, J. Al Latham Jr., wrote the subcommittee.

"The chairman's letter is misleading," Latham charged. He cited figures that showed Dennis' productivity equal to or better than Dotson's.

In a separate letter, Zimmerman said Dotson was "seriously distorting" his own productivity record, by counting some cases twice.

Charles M. Williamson, Dotson's chief counsel, quickly responded in a five-page letter to the subcommittee, saying that Dotson never intended to blame Dennis or Zimmerman, but, since they had written letters, he wished to set the record straight.

Williamson accused Latham of using "bad logic and worse judgment" and said Zimmerman's letter contained "specious and misleading" statements.

"Members Dennis and Zimmerman, as far as this office is concerned, have become involved in what I may describe, for want of a better phrase, as a unilateral quarrel," Williamson concluded. "Neither of them made any attempt to contact this office about their concerns prior to writing you and the subcommittee . . . . "

Three days later, Latham sent the subcommittee a short note. "Mr. Williamson's letter contains significant factural inaccuracies. It is obvious, however, that any attempt here to correct the record before the subcommittee, for a second time, would only result in further comment from the chairman's office. Accordingly, . . . I am available to meet informally with you . . . to answer any further questions."