First, the implication (that I read) in your post that there could be your App running without a Form instance created (so the "Message Pump" of the Application does not depend upon a Form) suggests a Windows Service might be the right choice of App structure for you. Just ignore this comment if I incorrectly interpret your post.
Second, the question of how to make a single-instance WinForms App is one many people have addressed:
1. Scott Hanselman presented a solution in 2008 using the Visual Basic Library in C#: [^
2. To use the Mutex ... which is, evidently, on your mind ... see the CodeProject article: "Single Instance Form Application in C#" December 2013: [^
By far the best example, and discussion, of the use of Mutex for a single-instance app I have seen is in Mark Michaelis' "Essential C# 4.0," Chapter 19.8. The sample code for that book can be downloaded (.pdf) here: [^
], and you will find his sample code in the Chapter 19 folder.
3. Chris Sells in his 2006 book on C# WinForms (Chapter 14) covers several interesting alternative ways to run a WinForms Application: [^
Chapter 14 is available as a free download (.pdf) here: [^
Note that this chapter does not cover creating a single-instance application; for that, Sells, like Hanselman, uses the Visual Basic Library, and that is covered in another chapter.