STATE COLLEGE, Pa. -- Penn State has released a document sought by some of its critics detailing the agreement with former FBI director Louis Freeh to investigate the Jerry Sandusky child sex abuse scandal, a review that cost the school about $8.1 million.

Including the bill to pay Freeh, Penn State's total costs associated with the scandal topped $41 million as of the end of December, the university disclosed Monday on a website.

The monthly financial update provided more itemization for certain costs, including the Freeh report. The update also counted the first of five annual $12 million installments -- paid in December -- that would ultimately cover the $60 million fine from the NCAA as part of landmark sanctions for the scandal.

Some vocal alumni had called on university leadership to release itemized costs, in part to promote transparency. Those critics had also asked the university to release the letter of agreement, or "engagement letter" with Freeh, that outlined the scope and responsibilities of the former FBI director in leading the internal investigation into the scandal.

The letter from Freeh was signed Dec. 2, 2011 by then-board chair Steve Garban and trustee Kenneth Frazier, who headed the trustees committee to which Freeh reported.

Freeh concluded that Paterno and three school administrators acted to conceal allegations against Sandusky to protect the school's image. The administrators have vehemently denied the findings.

Paterno died in January 2012. Last month, an exhaustive critique commissioned by his family called Freeh's findings inaccurate and unfounded, and resulted in a "rush to injustice."

That review raised new questions about the report and the university's handling of the findings from the alumni critics, some ex-players and a handful of trustees including the outspoken Anthony Lubrano. In particular, Lubrano has said the school should ask for a refund from Freeh because the investigation was not full or complete

The engagement letter outlined that Freeh's findings would cover why there were failures to report; who knew about allegations; and how the allegations were handled by trustees, administrators, coaches and other staff.

The report "also will provide recommendations ... for actions to be taken to attempt to ensure that those and similar failures to not occur again," read the letter posted by Penn State.

The school has said the findings were used to improve Penn State operations -- including how the trustees govern -- and that it was not within Freeh's scope to review actions or motives of other entities.

Lubrano joined the board in July, eight months after the scandal started. He praised the school for releasing the letter, but said "In my view, pointing to the recommendations is a deflection of the real issue.

"The real issue is that Freeh did not deliver what he was engaged to deliver, what he was paid to provide," Lubrano said Monday in a phone interview.

School spokesman Dave La Torre said the letter was released after multiple requests from alumni, and that "the board thought it was appropriate to do so."

He declined comment when asked if the release of the letter might answer questions from critics.

In a statement, the alumni watchdog group Penn Staters for Responsible Stewardship said the engagement letter's release was important because it showed the Freeh team's obligation was to the trustees and not the school itself, and that the report should be reviewed by the public and NCAA in a "far different light."

The board, as the university's governing body, brought in Freeh for the school, the school said in a statement through La Torre. They were not separate entities, and "there is no inherent conflict of interest between the governing body of an organization and the organization itself," the statement said.