There is actually no managed way to do that form of animation to the tray in native winforms, however you can P/Invoke shell32.dll to do it:
Some good info here (In the comments not the post):
http://blogs.msdn.com/jfoscoding/archive/2005/10/20/483300.aspx
And here it is in C++:
http://www.codeproject.com/KB/shell/minimizetotray.aspx
You can use that to figure out what stuff to Pinvoke for your C# version.