I am a non-EU citizen and work for a German company. We currently have a project in the Netherlands. I have a residence permit for Germany, and I would now like to get a BSN for the Netherlands, as I would be living there for extended periods. Am I eligible, or do I need to get a Dutch work permit? Mind you, I am employed in Germany and not the Netherlands. My passport is Australian.
If you live in the Netherlands, you almost certainly need a Dutch work and residence permit (the one exception that comes to mind is posted work but that's apparently not your status). The fact you are employed by a German company in Germany only makes formalities more complex but does not in itself exempt you from this basic requirement, which stems from the objective fact that you are residing there.
You can get a BSN has a non-resident but that's moot, even if you somehow managed to live in the Netherlands without one (which would make interaction with all public services difficult), you would still need a residence permit.