There are actually several studies on this.
A small study from 1999
found that flexible "colonoscopy does not adversely affect serum PSA levels."
A slightly larger study from 2004
drew this conclusion: "Flexible colonoscopy affect serum PSA (free and total) levels in certain patients. Special attention must be given to those patients with PSA levels in the 'gray zone' before colonoscopy."
Finally, the latest and largest study
(from 2010) found that "serum PSA levels were elevated during 7 days after colonoscopy."