I have not been able to find any DS with a serial number starting w "AD".
Hope you don't take offense but I couldn't find any Colt revolver that you might have likely mistaken for a Detective Special with a serial number starting w "AD".
Folks around here are usually very helpful so I imagine you haven't gotten an answer because they were also unsuccessful.
Worry not, someone will come along w the answer.
BTW, calling Colt is a good strategy