Is there statistical evidence of the benefits of CRM?
The benefits gained from CRM are not really applicable to a single pilot situation although solo pilots can apply CRM Ideals in their own regard. This FAA study touches upon it well in this study (numbers provided in the figures on page 2 of the study)


  Concern with the factors underlying these accidents led NASA
  researchers in the 1970s to conduct a series of interviews with line
  piLots to investigate their perceptions of aviation mishaps. Charles
  Billings, George Cooper, and John Lauber found that one mishap
  component consistently mentioned by pilots was inadequate training.
  Even more interesting, these researchers found that it was not
  technical training that these pilots felt they lacked, but training in
  leadership, communication, and crew management. In other words,
  traditional training had done an excellent job of imparting stick and
  rudder skills, but these pilots felt that they needed more training in
  crew oaordination. A subsequent analysis of jet transport accidents
  between 1968 and 1976 revealed more than 60 that involved problems
  with crew coordination and decision making (Cooper, White, &amp; Lauber,
  1979).


CRM solves the problem of their being two brains in the cockpit. In other words one of the primary issues they found surrounding aviation incidents was the fact that there were two pilots who had communication troubles in the cockpit (with each other). In some regards a counter point can be made that removing the second pilot is safer by eliminating these possible issues. The study makes it clear that pilots across the board had satisfactory skills in identifying issues and flying the plane but encountered issues efficiently communicating the issues in the cockpit. 

This is a tough topic as there are currently no single pilot certified airliners but there are some single pilot certified biz jets which makes that the next best place to look for info. A study was carried out on the difference in accident rates between single pilot and dual pilot situations which interestingly does not show a huge lean either way. The article does not talk about CRM but it could be a starting point for a meta study on CRM as it applies to that group of accidents. 

On any note Captain Sullenberger makes it clear that good communication and CRM were key to the successful outcome of his ditching. There is a great interview where he talks about it here. 

According to this paper poor CRM was one of the largest human factors in commercial accidents. 


  Within the preconditions level, CRM failures were associated with the
  largest percentage of accidents. Approximately 29% of all
  aircrew-related accidents were associated with at least one CRM
  failure.


I can't find a whole lot of direct evidence that CRM has made airplanes safer but the FAA tends to take the approach of identifying the large issues (of which CRM seems to be) then working the problem through training. It is far harder to isolate and subsequently measure human factors. Engines that stop running, brackets that fail, wires that short, etc. are much easier to study...