Ex-technical director Shane Sutton was found to have used sexist language towards Varnish, but was cleared of eight of nine allegations against him.
Varnish is entitled to see her records under the Data Protection Act.
The 26-year-old has requested access to Sutton's text messages and British Cycling's report into his conduct.
Earlier this month British Cycling found that Sutton had used the word "bitches" to Varnish, but the rest of her allegations, including a claim that he told her to "get on with having a baby", were not upheld.
Varnish said she was "shocked and upset" by British Cycling's decision on the majority of her complaints.
Varnish raced alongside Victoria Pendleton in the team sprint at London 2012, but failed to qualify for Rio 2016.
The World Championships medallist said that bosses at cycling's governing body were to blame for her and Katy Marchant not securing a team sprint spot at the Games. She added that their chances had been compromised by decisions over selection.
She was dropped from British Cycling's elite programme in April with Sutton telling the Daily Telegraph at the time that "there  is no point carrying on and wasting UK Sport's money on someone who is not going to medal going forward".
Sutton resigned in April, after being suspended pending the investigation.
Track cyclist Jess Varnish has demanded British Cycling release her personal data after she was subject to sexism at the organisation.