Max Weinstein looks at the question at Beyond the Box Score this week.
He ran several different tests and came to this conclusion:
As it turns out, the pitcher, and not the catcher, is the player with the higher propensity to influence the running game, whether in a positive or negative way.
Like in any thing, there will always be extremes. Despite our findings, exceptional talents like Johnny Cueto or Yadier Molna will continue to do what they do best. Generally however, the pitcher's overall and isolated CS% will be highly correlated to the battery's CS%.
Disregarding one's influence on the other is negligible, much like we do under conventional baseball thinking that the catcher is responsible for CS%. We need to go beyond conventional wisdom and accept that CS% is not a skill directly related to the catcher, but largely a function of the pitcher.
It was an interesting read for those of you who are interested in things like that.