Matthews was head of the Ministry of Transport when senior manager Joanne Harrison stole $725,000 through fake invoices made out to non-existent companies.
After Harrison was convicted and jailed earlier this year, the committee asked senior public servant Sir Maarten Wevers to review his suitability to remain in the role. Opposition members on the committee were concerned that they had not been told the full story of Matthews' handling of the fraud case.
Matthews, who received a draft version of Sir Maarten's report in June, resigned before the committee had made a decision about his future.
Speaker David Carter said today that the committee members "saw no value" in releasing the report because Matthews had stood down and put an end to the matter.
Carter said he could give an assurance that there was no criticism in Sir Maarten's report of the vetting process for Matthews.
He also ruled out any arrangement or settlement under which Matthews would agree to stand down on the condition that the report was withheld.
"No exit package was given," he said.
Public Service Association national secretary Glenn Barclay said the decision to withhold the report was "not good enough".
"The public need to feel that appointments to the office aren't made lightly, especially when an elaborate fraud case like this has been hanging over the people involved."
"ULTIMATELY RESPONSIBLE"
Sir Maarten's report was tabled in Parliament today.
An hour earlier, Matthews said that he had tendered his resignation.
"The issues and speculation about how I handled matters in relation to the fraud committed on the Ministry of Transport during my term as CEO have made it untenable for me to continue in this role," he said.
He said he deeply regretted and apologised for the fraud that was committed on his watch.
"I wished it had never happened but I accept I am accountable for everything done in and by the ministry when I was CEO and I am ultimately responsible."
He regarded Harrison as an "able and high performing member" of the ministry's leadership team until he received "concerning information" in April 2016.
"I believe I acted swiftly and thoroughly to detect the fraud and bring her to justice when I became aware of her potential wrongdoing. I wish that I had detected her criminal activity much earlier."
Matthews said he thought he dealt with the issue appropriately at the time. He said he should have been "more suspicious".
He felt "as angry and aggrieved as anyone" about Harrison's fraud.
"I have resigned as Auditor-General because I understand the expectations associated with this role are high. It is important to me, and to the office, that the public has complete confidence in the person holding the position of Auditor-General."
Matthews temporarily stood down two months ago while the investigation took place.
Opposition MPs who approved his appointment said they were not given all of the information about Matthews' handling of the fraud case during the vetting process.
As a result, the Officers of Parliament Committee agreed to a review of his "suitability" to continue in his job.
