This question already has an answer here:
Where can I find information if the german Dr.med. is corresponding to the USA PhD? Did anyone with Dr.med. apply for USA PhD equivalent?
Thanks for the comments. Actually I don’t really think this has been answered here. I read the mentioned topics and they don't answer my question. MD in USA is a title students get after finishing medical school. In Germany this turns you in a Physician, but you don't have the title "Dr.med." To earn the title you have to write and defend a doctoral thesis. That's why MD in US and Dr. med. in Germany are not the same.
About transfer from US to Germany it says (Grundsätze für die Regelung der Führung ausländischer Hochschulgrade (PDF) auf kmk.org.):
“Inhaber von folgenden Doktorgraden …Vereinigte Staaten von Amerika: „Doctor of Philosophy“ Abk.: „Ph.D.“,…können anstelle der im Herkunftsland zugelassenen oder nachweislich allgemein üblichen Abkürzungen die Abkürzung „Dr.“ jeweils ohne fachlichen Zusatz und Herkunftsbezeichnung führen.”
This is what I find on Wikipedia, but I hesitate to huse this as my only source:
"There are a variety of doctoral degrees, with the most common being the Doctor of Philosophy (PhD), which is awarded in many different fields, ranging from the humanities to the scientific disciplines. There are also some doctorates in the US, such as ... Doctor of Medicine (MD) ..., which are generally regarded internationally as professional degrees rather than doctorates, as they are not research degrees and no defense of any dissertation or thesis is performed. ...
...Doctorate degrees in Germany are research doctorates and are awarded via a process called Promotion ("promotion"). The concept of a US-style professional doctorate as an entry-level professional qualification does not exist. ...
...In German-speaking nations; most Eastern European nations..., the corresponding degree to a Doctor of Philosophy is simply called "Doctor" (Doktor), and the subject area is distinguished by a Latin suffix (e.g., "Dr. med." for Doctor medicinae, ...)."