I assume by "coordinate system", you mean GIS coordinate system that assigned to a drawing in AutoCAD Map 3D/Civil 3D, right?
To do that you need to set reference to AutoCAD Map 3D GIS platform API assemblies. Depending on the version of AutoCAD Map, the assemblies' name changes since it is officially available in AutoCAD Map 2009 (2008 had preview version).
Anyway, to find out the GIS coordinate system assigned to a drawing, you can do this:
However, when I ran this code in my AutoCAD Map 2009, GetMapSRS() sometimes does not return the coordinate system wellknown text on already opened drawing, even the drawing really has a CS assigned and I had to reopen the drawing. I have not tried this on later AutoCAD Map version. I am not sure it is the API bug in the early API version (Acad Map 2009) or my code error somewhere. Anyway, hope this be a little help.
BTW, for Acad Map specific, you may want to post to Acad Map Developing forum, but I guess a lot of regular visitors to this group may also actually use ACAD vertical like Acad Map/Civil anyway.