How to get current menu item “CSS Classes” value?

Do not know if it’s exactly what you’re looking for but this short snippet adds custom classes to nav menu item :

add_filter('nav_menu_css_class' , 'wpse_143574_nav_class' , 10 , 2);
function wpse_143574_nav_class($classes, $item){

         $classes[] = "my-class";

     }
     return $classes;
}

This could be modified with some conditional tags too.

EDIT: $item is often useful for example if ( $item->title == 'Contact')