Lying "Sacks" of ...
The tapes are said to show a simulated drowning technique
But ex-commission executive director Philip Zelikow says the CIA did not hand over tapes that have since come to light, the New York Times reported.
The CIA later erased the footage, which allegedly contains images of abuse.
The memo urges a further investigation into whether the agency acted illegally by withholding the recordings.
The CIA says there was no specific request for the tapes, which reportedly contained images of interrogation techniques including water-boarding, which simulates drowning. The CIA denies torture.
The agency filmed the footage in 2002 and erased it in 2005, a year after the commission ended its work.
The commission conducted an internal review earlier this month after the deleted CIA tapes came to light.
A copy of Mr Zelikow's findings, dated 13 December, was obtained by The New York Times.
His memorandum notes the commission asked the CIA in 2003 and 2004 for "documents", "reports" and "information" relating to interrogations.
But, the report says, a CIA director replied in 2004 that it had already "produced or made available for review" all relevant material.
Mr Zelikow's seven-page findings conclude "further investigation is needed" to determine if the CIA's withholding of the tapes violated federal law.
It notes that it is illegal to "knowingly and wilfully" withhold or "cover up" a "material fact" from a federal inquiry.
The CIA insisted on Saturday it had gone to great lengths to help the commission, which was set up to investigate al-Qaeda's 11 September 2001 attacks on the US.
The agency's spokesman Mark Mansfield said: "Because it was thought the commission could ask about tapes at some point, they were not destroyed while the commission was active."
But one of the commission chairmen, former Democratic congressman Lee Hamilton, told the New York Times the CIA had "clearly obstructed" the commission's work.
The CIA and the Department of Justice have already launched an inquiry into the erasing of the tapes.The agency said the footage was deleted to protect the identities of agents and because it was no longer of intelligence value.