Erie County New York (Buffalo), under County Executive Chris Collins implemented Six Sigma. I was not personally involved with the Erie County Six Sigma effort, but you can learn more about the projects worked on at http://wwww.erie.gov/exec/?reform-government/lean-six-sigma-initiat....
Six Sigma was implemented in Erie County by Chris Collins a private business person who never held elected office before. Collins arrogant personality and disdain for working with the County legislature, left a bad taste in a lot of people's mouths regarding Six Sigma. In fact Collins was not re-elected and I expect the new County Executive, will move away from continuing the program.
Personally I think Lean, which I view somewhat as Six Sigma lite is a better fit for implementing change in government. Six Sigma's statistical analysis, belts etc. are too complicated for a government non-profit generating operation.
The Lean emphasis on eliminating process steps, eliminating waste, reducing cycle time etc. without all the heavy stat charts is a better fit in my opinion.