If the allegations are true, they would run counter to the conclusion of General Motors' internal investigation, which blamed incompetence as the primary reason the automaker approved the use of faulty ignition switches, and then was slow to recall them once it learned of accidents.
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"We believe the documents show, and the testimony that will come out that this wasn't incompetence, it was a cover-up," Cooper said.
General Motors did not immediately respond to CNBC's request for comment on the allegations.
In the conference call with reporters on Monday, Cooper said the evidence to support his allegation will come out when the first class action lawsuit surrounding the defective switches takes place in January.
Attorneys are already in the midst of discovery and are exchanging documents. Later this year, Cooper said he expects former and current GM engineers and executives to be deposed about what they knew regarding the faulty switches.
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"Beginning in May and running throughout the end of the year, depositions of all important General Motors witnesses will be taken, including high-level executives," he said.