If you want the labels in CAD, here's a workaround (you're not being very specific as to what you're trying to accomplish). In ESRI, create a point file for the centroid of each label. Populate the label field in the attribute table.
Next, in a "map capable" version of AutoCAD, tpye "mapconnect" in the command line. This will bring up the screen shown below (I'm assuming you know how to manage coordinate systems in CAD). First, select "Add SHP connection". Next, click the SHP ellipsoid (shown with #2) and navigate to the location of your point shapefile. Lastly (step #3) hit the connect function, and inside that menu, hit "add to map" Now all you need to do is make your points invisible and turn on the labels (which will require you to switch to a Geospatial interface in CAD -- shown in next printscreen).
There are Geospatial functions available in CAD. Under the arrow highlighted below, you can see that there are Geospatial functionalities inherent to CAD (map capable versions that is). The icon looks very much like a gear (Beside "Dano1" in my printscreen). This menu can be found in the bottom right portion of your screen. If you get this far and are not sure how to proceed, the only this I can suggest is that you post another question related to labeling spatial data in CAD.