EMPLOYEE0No, you cannot share contacts with other users as you can with documents and calendars. At least not right now. This is a feature request that has already been suggested to Google.
There are some third party apps that do this. You can check out the Google Apps marketplace for more information.
Depending on what you're looking for, you could request a Google group for your department/workgroup. A Google Group provides a single email address to use for your entire department/workgroups. Once IT creates the group for you, you will have full control to manage who is in the group and who can email the group. Members of the group could then see a list of names and e-mail addresses of the other members in the group.