Does Autopilot make planes safer?
Using e.g. Boeing's annual commercial aviation safety statistics, one can essentially show that with each new aircraft generation, the accident rate reduces. This answers your question about statistic involvement, but doesn't really confirm a causal relationship, since it's not only automation but e.g. also human machine interface (flight deck) design and system architecture that improves. However, I would assume there are quite probably at least some safety improvements due to automation in there. One would need to go about analysing the accident factors to prove this.

As an interesting aside touching on this topic, a former colleague of mine flying commercial jets recently offered his first-hand view on different aircraft automation levels in his blog.

While not a comprehensive answer as such, I hope the links allow you to pursue this a bit further.