No, Post Bank was sold to Deutsche Bank. It was created by the Deutsche Post, who then spun it off, funneled a lot of their branches into it (so you have bank offices that also rent out a desk to the Post) and sold it to Deutsche Bank.
I think the name Deutsche Bank makes it even more confusing. As opposed to Deutsche Telekom (T-Mobile), Deutsche Bahn (DB/Schenker/Arriva) and Deutsche Post (DHL), Deutsche Bank never was state-owned. It was just named that way, because it was founded as a project (and arguably still is) so Germany would play a role on the world financial stage.
