A mutex is a Windows kernel object (here wrapped in a .NET object).
As such, it is an unmanaged resource that should be disposed.
More accurately, the .NET object contains a HANDLE to the mutex, which must be released/disposed of somehow.
I don't trust that code sample in the Mutex class docs where the mutex object is not disposed. Although Henzi has a good point in comment: The Mutex object is static and would be either disposed by the finalizer or destroyed by the Windows kernel when the process exits.
Also, note that Close() disposes the object as well.
Of course, there's nothing wrong with keeping an existing Mutex object in your app even while you don't use it. They are light resources.
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