If you use the Mutex(bool, string) overload to specify a name and initial ownership, it looks like there is no way the creator can actually know if they own the mutex after they create it. If another party has already created the mutex and has ownership of it, the constructor doesn't appear to throw an exception if the caller fails to get ownership, and there doesn't appear to be a way to query the resulting object, either.
So this overload should probably be avoided if you aren't certain you are the first to create the named mutex.