What do you mean by civil defence? Protection against catastrophes or Security agencies? Well, the former is organized in Germany at the federal level by the THW (Technisches Hilfswerk, Technical Aid-Agency), but there are also broad competences at the state-level. Our interior minister tried to change this, because floodings usually don't stop at state-borders, but some states were reluctant to give up competences

. But I don't know exactly how this is organized in detail. If you're interested in this, I can try to find some english-language homepages to that issue.
With security agencies it's largely the same: There is a federal agency, the BKA (Bundeskriminalamt, Federal Criminal Agency), and a federal police (Bundespolizei), but the main competences are also at state-level. And our interior minister also tried to change this. And some states are also reluctant to give up competences...