@Anke, let me respectfully disagree...
as already said earlier
see also this Stackoverflow answer
You can ask the user to select a folder (which will be under the restricted public locations) and then you can programmatically access and check and files in this location. See Access documents and other files from shared storage | Android Developers
You can ask the user once and then store the permission they have given you to access files/folders with Access documents and other files from shared storage | Android Developers
Taifun