The revelation in a U.S. District Court affidavit filed by Kilpatrick contradicts what city lawyer John Schapka said last month responding to a civil lawsuit filed by the family of slain exotic dancer Tamara "Strawberry" Greene.
Schapka said computers belonging to Kilpatrick and his former mistress, former chief of staff Christine Beatty, were thrown away and replaced in February 2008.
The civil suit alleges Kilpatrick and other city officials blocked the investigation into the murder of Greene, who allegedly had danced at a party at the mayoral mansion and allegedly was assaulted by Kilpatrick's wife.
Cockrel says he does not remember Kilpatrick leaving a computer behind in the mayor's office.
"My recollection is when I moved into the mayor's office, there was not a hard drive there," Cockrel told The Detroit News.
The computers were thrown away, Schapka said, even though Kilpatrick was facing lawsuits over e-mails and text messages that ultimately led to his resignation.
A lawyer for Greene's family has requested a default judgment against the city for intentionally throwing away Kilpatrick's computer.