Case of such a setting to Custom Post Type in a your Multisite now.
A description of how to make this case.
First I will explain how to do.
Then I will explain the cause.
How to do
I’m using this Custom Post Type UI plugin.
 In each site to create each custom post type to use.
 Create default site of all custom post type.
First, You create the default site a custom post type of all.
 Setting the all Custom Post Type to be used in all sites in the WP Admin UI Customize.
 Hide custom post type to the use the default site.
It allows you to display menu like this in this.
Default site do not have any other custom post type.
Therefore it is not possible to select a menu from the WP Admin UI Customize.
The unified master site
It is a feature this.
Custom post types of other sites.
I will consider the function so that you can drag from the list.
For example, in this way.
I’m sorry, I can not still this. Because get_post_types() is can not get in on Network.