Cohen officially became a co-sponsor of the measures before leaving Washington last weekend, becoming the most recent Democrat to join the impeachment movement started by Rep. Dennis Kucinich, D-Ohio, the Memphis Commercial Appeal said Tuesday.
Kucinich introduced a resolution, that would also censure Cheney and President George W. Bush, in April and it has since garnered the support of 18 Democratic co-sponsors.
The impeachment process is oriented around Cheney's alleged involvement in several secret detentions and for his support of a U.S. wiretapping program.
Cohen said Monday that he has also begun an impeachment process against U.S. Attorney General Alberto Gonzales for his part in such activities.
"I just think that with what I've seen in these first seven months is that there's been so much disregard for the Constitution by the administration," Cohen said. "I've seen it firsthand on the Judiciary Committee with General Gonzales."