To get married in Denmark you need to send an application for a certificate of marital status to the Agency of Family Law. Unless both you and your partner meet one of the following criteria:

• You are a Danish citizen
• You are a citizen in a Nordic country (i.e. Finland, Sweden, Norway or Island)
• You have a permanent residence permit, issued in Denmark
• You have an obtained a permanent residence right under the Directive 2004/38/EC implemented in Danish law as “EU-Opholdsbekendtgørelsen”

In that case you need to apply for a certificate of marital status at the local municipality.