Jim,
You can import object data into CAD with the mapimport command. While in CAD type- mapimport. Browse to the file you would like to open. When the map import dialog box opens, be sure to click in the 'data' box. See attached image. Once you click in the data box you can see an add button pop up. Click this, and a attribute data box will appear. In the attribute data box select 'Create Object Data', and in the drop down select the object data for your shapefile. Thats it. Hope this helps.
Dustin