All US passport holders on semester or academic year programs in Denmark must apply for a residence permit. All students must to travel to Chicago (or their nearest convenient processing center) to submit their materials, and to have biometric readings taken. You cannot start this process until you are officially accepted by the University of Copenhagen and have your acceptance letter. Below are the instructions, tips, and things to keep in mind for the application process.
If you are not a US passport holder, contact a Danish Embassy or Consulate and ask about your specific requirements.
Direct all questions about the residence permit application process to a consulate.