Microsoft Word does not support the sharing of a single Normal.dotm file among multiple users. This is true whether or not the file is marked as read-only.
The Normal.dot file stores user-specific settings and is not designed to be shared among multiple users on a single computer or over a network. Word accesses the Normal.dot file at various times and makes changes to it based on the user's actions. As a result, Word must have full read and write access to the file at all times.
For items that must be shared on a single computer, create a global template and put it in the office startup template folder or in the workgroup template folder. For more information, see How to manage templates in Office programs.