class CefCustomObject
{
    private static ChromiumWebBrowser _instanceBrowser = null;
    private static Form1 _instanceMainForm = null;

    public CefCustomObject(ChromiumWebBrowser originalBrowser, Form1 mainForm)
    {
        _instanceBrowser = originalBrowser;
        _instanceMainForm = mainForm;
    }

    public void showDevTools()
    {
        _instanceBrowser.ShowDevTools();
    }

    public void hideApp()
    {
        Form1 fullScreenForm = new Form1();
        fullScreenForm.WindowState = FormWindowState.Minimized; //не работает

        _instanceMainForm .WindowState = FormWindowState.Minimized; //тоже не работает
    }

    public void closeApp()
    {
        Environment.Exit(0);
    }

    public void opencmd()
    {
        ProcessStartInfo start = new ProcessStartInfo("cmd.exe", "/c pause");
        Process.Start(start);
    }
}

<div class="btns" onclick="cefCustomObject.hideApp();">

public void hideApp()
{
    _instanceMainForm.Invoke(new MethodInvoker(() =>
    {
        _instanceMainForm.WindowState = FormWindowState.Minimized;
    }));
}