Neighbor's tree - Security and dirt. Who is responsible?

Yes, I read it as long as you cut off the overhanging branches until the tree leans towards the neighbor’s side ;)

Karlsruhe decides on Berlin neighborhood dispute Is it allowed to prune the intrusive tree?

Der Tagesspiegel reports...

That was in the news yesterday or the day before, right?

I don't know, I got it from the Checkpoint newsletter of [Tagesspiegel].

I would hire an arborist. In any case, after you have already received an OK from the neighbor to remove the overhanging branches. Then you can prove in case of emergency that you acted knowledgeably. An arborist also knows the neighborhood rules regarding pruning. Of course, it costs a bit but not that much. It's better than dealing with latent trouble.