The trial was postponed to Thursday, to give the defence team time to peruse documents obtained from the State.
Mpembe, Gideon van Zyl, Dingaan Madoda and Oupa Pule are facing charges of contravening the Independent Police Investigative Directorate Act, defeating the ends of justice, and contravening the Commissions Act.
The four policemen were arrested after an investigation by the Independent Police Investigative Directorate (Ipid) which found that one mineworker, Modisaotsile van Wyk Sagalala died in police custody and not in the hospital or at the scene when the police shoot dead 34 mineworkers on August 16, 2012, in Marikana.
The mineworkers had been on a wildcat strike demanding to be paid a minimum of monthly salary of R12,500.
The State charged that they lied during the Farlam Commission of Inquiry that investigated the killing of mineworkers, they failed to report Sagalala's death, in that way contravening the Ipid Act and defeat the ends of justice by passing his death to appeared that he died in hospital.
It was only after Ipid investigation that a case was opened in February 2017 and they were arrested in March 2018.
Defence team consisting of advocate Jan Ellis appearing for Mpembe and Van Zyl and advocate Michael Ramashaba for Madoda and Pule had argued that the two dockets have a link with the current trial, and were relevant for the trial going forward.
Lead Prosecutor Jacob Tloubatla had previously mentioned that the dockets requested were not relevant for the matter in court.
The defence and the State could not reach common ground on the said dockets and on Tuesday, Judge Ronnie Hendricks ruled that the State should disclose the dockets to the defence.
During a brief court proceeding on Wednesday, the state and defence confirmed the dockets have been disclosed.