get parent category

You will need to use the ID value returned by $category[0]->category_parent and pass it through get_term()

$category = get_the_category(); 
$category_parent_id = $category[0]->category_parent;
if ( $category_parent_id != 0 ) {
    $category_parent = get_term( $category_parent_id, 'category' );
    $css_slug = $category_parent->slug;
} else {
    $css_slug = $category[0]->slug;
}

//ref:https://wordpress.stackexchange.com/users/8054/rachel-baker