the easiest way is to ask the Standesamt why the need proof of financial situation. Otherwise I can only guess.
Basically said: There is no law that you have to prove your income when wanting to marry.
My guess is: You need a "Ehefähigkeitszeugnis", you cannot bring it, this is why you need to be excempted from this rule by the Oberlandesgericht. The court (Oberlandesgericht) charges a fee that depends on your income.
See here for more information (I took OLG Köln as example)
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