As an EU/EEA citizen or Swiss national, you may stay in Denmark for up to three months without a residence permit. If you work while you are here, you can stay up to six months. If you stay longer, you will need either a registration certificate (for EU/EEA-Swiss citizens) or a residence card (for Swiss nationals).
How to obtain a registration certificate
The registration certificate or residence card may be obtained at the Regional State Administration
The application must be submitted within three months after the entry into Denmark. Note that it may take up to three weeks to process your application and issue your permit.
Unlike a residence permit issued under the Danish Aliens Act, these documents are merely proof of your existing rights under EU rules on the free movement of people and services.
If you are a citizen of Finland, Iceland, Norway or Sweden, you need not apply for a registration certificate because as a citizen of a Nordic country you have a right to reside in Denmark without permission.
Regional State Administration
The Danish Immigration Service
Who are Union citizens and EEA nationals?
Union citizens are nationals of Austria, Belgium, Bulgaria, Cyprus (only the Greco-Cypriot territory), the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, the Netherlands, Poland, Portugal, Romania, Slovakia, Slovenia, Spain, Sweden and the United Kingdom.
EEA nationals are nationals of Iceland, Liechtenstein and Norway.
Nationals of Switzerland are covered by the same rules as Union citizens and EEA nationals. Accordingly, all the rules mentioned also apply to Swiss nationals.