You'll probably have to mill threads. This doesn't use a tap, but rather a cutting tool with the thread form. The cutting tool is smaller (in this case 3.8mm) than the hole, so it's inserted, and moved in a circular fashion to cut threads around the hole.
You will need a CNC milling machine, to perform this. Sandvik provides some information on the process (Not affiliated in any way). Thread milling also means that there's no risk of destroying the part with a stuck tap.
A well equipped machine shop can do this milling for you.