RTS, where two former employees are under investigation over manipulation of quality control data on forensic samples, has also insisted that it was the whistle-blower over the issue.
Last month it was revealed that the investigation into Mr Atkinson's death, being carried out by the Independent Police Complaints Commission, had been delayed over fears that toxicology samples had been "compromised".
In a statement read out at Mr Atkinson's pre-inquest review it was revealed that the IPCC used a company called Key Forensic Services to provide data for its investigation into the death of the former Aston Villa player.
The company allocated toxicology analysis to RTS, as it had no capacity to perform the service.
Avon and Somerset Police force has now been ordered to retest samples taken by RTS in police investigations.
The case is one of thousands of cases believed to have been affected by the situation.
In a statement RTS said: "RTS is currently managing the process of retesting samples at appropriately accredited laboratories, as well as covering the associated costs.
"Two former employees remain on police bail. All appropriate pre-employment checks were conducted."
The company has also insisted that it discovered the problem and alerted the authorities to its concerns.
A statement said: "RTS is the whistle-blower in this issue of forensic manipulation.
"In January 2017, RTS investigated an anomaly in a forensic report, identified manipulation of quality control data and immediately reported this to the police, accreditation agency and the forensic science regulator.
"This activity had not been identified in numerous external audits by the accreditation agency, other forensic science providers, or by defence experts in numerous cases.
"RTS are working with Greater Manchester Police, the Forensic Service Regulator and the Home Office to resolve the situation. The investigation now dates beyond RTS to laboratories which are unconnected to it. However, it was RTS action that identified this activity."
Mr Atkinson, 48, died after being shot with a police Taser outside his father’s house in Meadow Close, Trench, on August 15 last year.
The retired footballer became unresponsive and died despite the efforts of hospital doctors who battled for 35 minutes to try and save him.
In August, it was revealed that three police officers have now been interviewed under criminal caution.
But the IPCC says the criminal investigation does not necessarily mean criminal charges will follow.
The three West Mercia Police officers were earlier served with gross misconduct notices.