Unless you have added the functionality with a plugin or custom code, Pages are not placed in Categories. Pages are organized with Parent Pages and Children Pages. This is why (I suspect) in_category() does not work in page.php
The following code in functions.php will add categories to Pages.
/**
* Add categories to Pages.
* from http://shibashake.com/wordpress-theme/add-tags-and-categories-to-your-wordpress-page
*/
function add_custom_tags_box() {
add_meta_box( 'categorydiv', __('Categories'), 'post_categories_meta_box',
'page', 'side', 'low');
register_taxonomy_for_object_type('category', 'page');
}
Hope this helps.