What there is (afaik) is included in the IDE download in the "reference" directory.
It's all HTML, and duplicates the "Learning/Reference" page on the website. It doesn't fully document C, avr-libc, or C++, just the pieces that are seen as important to beginners, and the specific arduino library functions.
Real arduinos will not run C#, but there have been a couple similar boards that do. Notably, "Netduino": http://www.netduino.com/hardware/ Ray's comment is appropriate: the latest netduino boards use a microcontroller with 1MB of flash memory, and they have ~384kB left for your programs once the .net framework is loaded on them (Still, since the end prices are close to the much smaller arduinos, you might not care.)
You can, of course, communicate with the Arduino using the Serial object. My guess is that if you search the Code Project web site you can find C# code for the Arduino. I just searched "Arduino and C#" and was returned 205 results. Perhaps one of those will help.