I am a US/German dual citizen about to start studies in Switzerland in a month. Previously, I traveled in Europe for about 2 months on a US passport. While in Europe, I received a German passport. I plan to leave Switzerland in 6 months and travel back to the US. I am aware that US citizens are given only 3 months in the Schengen zone. Will this lead to any complications even if I leave on my German passport? Will either of my passports be affected?
As an EU/EEA/Swiss citizen, you have a nearly absolute right to enter the Schengen area and as such you cannot be fined for "overstaying" on your US passport. You having this right is a property of you as an EU citizen and having a German passport is simply a way of demonstrating that fact.
Also note that Schengen border control officers routinely forget to stamp passports at exit immigration so there are tens of thousands of travellers out there with no proof of exiting the Schengen area. While this could be a problem for non-EU citizens, there is no reason for you to be concerned about this matter.
The only problem I can see regarding the passports is that the "trail of stamps" on your US passport shows you still in Schengen. This could irritate some third country visa officials, but not those from the Schengen zone (if you show them your German passport, old stamps are no issue).
- I presume that you got a fresh German passport, not a fresh citizenship, or the dual citizenship might be a problem.
- In the future it would be a good idea to use the German passport to enter the EU, fewer complications and questions that way.
- If you are worried that your German passport might expire at an inconvenient time in the future, you can apply for a German identity card even if you are not resident in Germany. It might be clever to get one in a few years, so that the validity periods of the passport and the identity card overlap -- if the passport is just expired the ID card is still valid, and vice versa. The ID card allows you to travel in the EU and some other countries. Of course that means going through the renewal twice that often, so YMMV.
As a German citizen, you do of course have the right to enter, leave and stay in Germany as you please.
In practice, you shouldn't have problems using the German passport for the EU in the future.
However, you should assume that your US passport is "in the system", and will be marked as overstayed. Note that passports are usually electronically scanned at border crossings - wether or not you get an actual stamp. The Schengen does not have an electronic entrance/exit database (yet), though you still may be questioned if you miss the exit stamp.
You could also just go on a brief trip outside the Schengen to get the exit stamp, and re-enter on the German one.
Nevertheless it makes sense to use the German Passport any EU travel in the future, to avoid any misunderstandings (US law requires you to always use the US passport when going there).
For third countries, it makes obvious sense to always use the passport that is most convenient for the destination country...
If you're living abroad when your German passport expires, you can renew it at the German embassy.
Disclaimer: Nothing I say should be taken as professional legal advice. If you have doubts, ask a legal counsel. Especially true if you just naturalised; in this cases there arcane rules to retaining dual citizenship, which are beyond the scope of this answer.