When I married my German wife, I was required to produce evidence of the fact that I was unmarried (note: not
single) in my country of birth. German bureaucrats refered to this document as an
Ehefähigkeitszeugnis.
As the Standesamt cannot check whether foreigners are legally married in its own records (Heiratsregister), all non-Germans wishing to get married under German law as required to provide evidence that they are unmarried (translated and notarized unless this is not necessary under some bilateral agreement).
You'll have to judge whether this is (roughly) equivalent to your "Affidavit of Single Status".
Edit: I procured the necessary document from the Department of Internal Affairs, i.e. for an official government source. A Columbian friend of mine faced the problem that births, deaths and marriages are church matters in Columbia, i.e. the 'official' documentation is done by the church. The Standesamt refused to recognize his non-official documents, and the betrothed resorted to getting married in Denmark.
