Both men were chosen to serve in the Senate by Prime Minister Stephen Harper.
The affidavits were filed in an Ottawa court on Tuesday.
In the affidavit pertaining to Duffy, Cpl. Greg Horton says he believes Duffy "hired a friend as a consultant over an approximate four year period, and paid him a total of approximately $65,000 during that time, for little or no apparent work."
Horton said in the affidavit that the friend, Gerald Donohue, was interviewed by investigators "and acknowledged that he produced no tangible work product for Duffy."
Donohue told investigators that he did internet research and provided verbal advice to Duffy, Horton wrote.
The RCMP needs the banking records to prove where the money went, Horton wrote, because Donohue says he never saw any of it, and that it went to his business.
"The supporting documentation relating to the bank transactions will assist investigators in identifying where the money went after it was deposited, and who received the money if Donohue did not," Horton wrote.
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