I don't know about all types of Behörde stuff, but I do know that it does not need to be notarized for the Anmeldung as I've done this before.
To be honest, I think a lot of Behörden are very informal about stuff (even though technically they are not supposed to be), so I would not give any general advice on this. I know I was able to deregister my second Wohnsitz by e-mail (i.e. without signing anything) and they sent me a jpeg of the confirmation, and I just also applied for the second ballot for the Landrat election by e-mail (to have it sent to the same address as the first ballot), but not all Behörden might be so nice about it, I would never tell anyone they can definitely deregister by e-mail, even though I was able to.
Edit: I know not all places require a notarized power-of-attorney which is why I said to call and ask. However, if in doubt, and if it is about important matters, I'd rather get the notarized power-of-attorney and be over-prepared than somehow not be able to get something important done because the Vollmacht was missing the notarization.