For private flights in Germany, the A1/A3 is not required as a DMO customer.
For flights in other European countries and for a take-off weight of 250 gr or more, you need the proof of competence A1/A3 of the LBA (Luftfahrtbundesamt). This costs 25 Euro and is valid for 5 years.
For commercial flights you always need a proof of competence.
More about the EU proof of competence