A botched overhaul at the government’s auditing regulator heightened an “environment of fear and distrust” among the staff that led to whistleblower allegations and the ouster of the board’s chairman, according to an official report that the Securities and Exchange Commission commissioned but then kept secret.

The January report by former SEC Chairman Harvey Pitt lays bare deep divisions within the Public Company Accounting Oversight Board, which oversees the audits of companies valued in total at trillions of dollars.

It also alleges organizational dysfunction. There were no records documenting the rationale for several staff firings, and confusion about the roles of the PCAOB’s board members has “created some dysfunctional behavior” by them, the report found.

New SEC Chair Gary Gensler this month ousted William Duhnke as PCAOB chairman, and is in the process of replacing the rest of the five-member board.

A PCAOB spokeswoman didn’t immediately return a request for comment. An SEC spokesman declined to comment. Mr. Duhnke said he hasn’t seen the report and therefore cannot comment on it.

Mr. Pitt, who ran the SEC from 2001 to 2003 during the Bush administration, was commissioned by the SEC to investigate how the PCAOB was run following whistleblower allegations in 2019. The whistleblower alleged that Mr. Duhnke was pushing out longstanding executives, in some cases out of retaliation, and engaged in a politicized attempt to run down the watchdog.

The SEC is investigating Mr. Duhnke over his handling of internal complaints, The Wall Street Journal this month reported. He has denied any allegation of wrongdoing, saying he was making long-overdue changes at the organization and was the subject of a “well-coordinated smear campaign.”

The Pitt report says a “lack of sensitivity” on the part of Mr. Duhnke, his staff, and the other four board members created a “cultural angst” that led to the whistleblower complaints. The board failed to consider the impact on the staff of firing seven senior officials, and several midtier ones, without warning or explanation, the report finds.

But the report clears Mr. Duhnke, a former senior Republican congressional aide, of any political intent in his efforts to modernize the watchdog. The decisions on firing senior staff were taken by the board as a whole, the report finds.

That conclusion is disputed by some people close to the PCAOB whistleblowers. Mr. Pitt was viewed by Mr. Duhnke as an ally, those people say. Mr. Pitt resigned as SEC chairman in 2002 following a political firestorm that involved the PCAOB. Mr. Pitt said he was “fiercely independent” and not anyone’s ally in his review of the PCAOB

Mr. Pitt’s report concludes that the PCAOB needed shaking up when Mr. Duhnke came on board, but the execution was the problem. Mr. Duhnke was part of a new board appointed in 2018 after the PCAOB was rocked by an exam-cheating scandal, in which prosecutors said KPMG auditors colluded with a former PCAOB official to get a sneak peek at regulatory inspections. KPMG in 2019 paid $50 million to the SEC to resolve allegations related to the scandal, and said it had learned important lessons.

The report found the watchdog has been slow to update its ethics code after the scandal. “The board has not treated this project as a critical priority,” which was a mistake, the report said.

The report was delivered to the SEC in January. But the agency didn’t publish it or share it with the PCAOB, according to people close to the watchdog.

North Carolina Rep. Patrick McHenry, the top Republican on the House Financial Services Committee, obtained the report after requesting it from the SEC. In a letter dated Monday, Mr. McHenry wrote that the committee was investigating the SEC’s decision to overhaul the PCAOB. It wasn’t immediately clear whether House Democrats, who control the committee, would co-sponsor the inquiry.

Write to Jean Eaglesham at jean.eaglesham@wsj.com and Dave Michaels at dave.michaels@wsj.com