Hi Hendrix,
The DWP's current position seems to be that CFS/ME can have both physical and mental aspects, so both tests should be carried out.
This is the
current DWP guidance on whether CFS/ME is a physical or mental health condition in relation to DLA.
If you do have a separate mental health condition, such as depression, however, then it would certainly be worth getting a diagnosis from your GP.
Good luck,
Steve