Denmark - Work permit
The application for a work permit is carried out in conjunction with the residence permit. Once the residence permit is granted you are allowed to work in Denmark, which is extended also to any other member of the family (accompanying spouse and dependants), for which a residence permit has been obtained.
Anyone with a residence permit in Denmark, is allowed to work.
The authority dealing with residence and work permit is the Danish Immigration Service, a department under the Ministry for Refugee, Immigration and Integration Affairs.
To learn about residence permit procedure read the article Denmark - Visa.