ApplicationMutex.cs

public class ApplicationMutex : IDisposable
{
    private static readonly ILog logger = LogManager.GetLogger(typeof(ApplicationMutex));

    // This needs to have the prefix "Global\" in order to be system-wide
    public const string MutexName = @"Global\MyApplicationNameMutex";

    private Mutex mutex;
    private bool acquired;

    public bool TryAcquire()
    {
        if (this.acquired)
            throw new InvalidOperationException("Mutex has already been acquired by this process");

        try
        {
            // I think either of these calls can throw, so put them both inside the try
            if (this.mutex == null)
            {
                this.mutex = new Mutex(initiallyOwned: false, name: MutexName);
            }

            this.acquired = this.mutex.WaitOne(0, false);

            logger.Debug($"Queried mutex. Acquired: {this.acquired}");
        }
        catch (WaitHandleCannotBeOpenedException e)
        {
            logger.Warn($"Could not query mutex: {e.Message}");
            // There's probably a win32 object with the same name but a different type.
            // The only semi-sensible thing we can do is count this as "could not acquire"
        }
        catch (UnauthorizedAccessException)
        {
            logger.Info("Unable to query mutex: UnauthorizedAccessException");
            // We might not have permission to even read stuff about the mutex, in which
            // case someone else has acquired it.
        }
        catch (Exception e)
        {
            logger.Error("Unexpected exception when acquiring mutex", e);
        }

        return this.acquired;
    }

    public void Dispose()
    {
        try
        {
            if (this.acquired)
            {
                this.mutex.ReleaseMutex();
                this.acquired = false;
            }

            this.mutex?.Close();
        }
        catch (Exception)
        {
            // not much we can do at this point.  But, when process finishes exiting, the mutex will
            // be closed by the OS anyway.
        }
    }
}