I was stationed in Germany, with a rental property in NC, as an Alaska resident, so I can tell you what I experienced:
US Federal Income Tax: Schedule E every year, if I had economic net income it was taxed as ordinary income in the US
North Carolina: Had to file a non-resident return for the years that I made money. Only taxed on my NC source income (just the property).
Alaska: No state tax
You'll have to ask a German tax specialist if you have any obligations under the German tax code.