Officially, top and side menus can only include Section, MegaMenu, and MenuItem objects, none of which can be rendered like an input. However, you can manually attach your input to the menu using Application server-side event "onRendered" like this:

use \koolreport\dashboard\Application;

class App extends Application
{
    ...

    protected function onRendered($view)
    {
        //Insert input html and javascript into $view string at the top menu position
        ...
        return $view;
    }
}
 

You can inspect Dashboard's top menu element to see where input content should be inserted.

http://localhost/KoolReport/GitHub-documentation/dashboard/events/