The law[0] in question specifically says that the federal government has to authorize the prosecution.
[0] http://www.gesetze-im-internet.de/englisch_stgb/englisch_stg...
[0] http://www.gesetze-im-internet.de/englisch_stgb/englisch_stg...
(By the way, prosecutors are anyway bound to instruction in Germany (usually by the state governments). That doesn't mean the governments should actually use that power.)