The home secretary told MPs that "some work" had been done to ensure material was not included in the report which could damage national security.
But she said claims she discussed it with US officials were "inaccurate".
She said was not aware of "any evidence" the UK had been involved in torture, which she said was abhorrent.
The US Senate report, which alleged the "brutal" interrogation and treatment of al-Qaeda suspects in the wake of 9/11, contained no reference to UK agencies.
After it was published last week, Downing Street initially said no requests for redactions had been made but later stated that  requests were made by British intelligence agencies to the CIA for reasons of national security.
The government has insisted none of the details blacked out were related to British involvement in the mistreatment of prisoners.
Appearing before the Home Affairs Select Committee, Mrs May said suggestions that she or her officials had met Senator Dianne Feinstein, who chaired the inquiry, on multiple occasions in recent years to discuss the report were "wrong and inaccurate".
She added: "I have not asked for any redactions. Any such request will only have been in relation to the need to ensure that nothing damages our national security."
Asked about the case for a public inquiry into any UK complicity in illegal activities, Mrs May said the US inquiry had been conducted by the US Senate and it was appropriate for Parliament's Intelligence and Security Committee to continue its work.
The security services, she stressed, would co-operate fully with the investigation, adding that the committee was "not tainted by party political issues in the way it does its job" and acted "with integrity and thoroughness".
Keith Vaz, the Labour MP who chairs the cross-party Home Affairs committee, said he would be asking Mrs Feinstein to appear before MPs herself next year.
Theresa May has said she did not ask for any details about the UK security services to be redacted from a report about alleged torture by the CIA.