As an EU citizen you may freely enter Denmark and remain in this country for up to 3 months without an EU residence document (registration certificate). If you are a job-seeker, you may reside in Denmark for up to 6 months without a registration certificate. The periods of 3 and 6 months are calculated from the date of entry.
If you expect that your stay in Denmark will last more than 3 months, you have to apply for an EU residence document before the expiry of the three months.
For more information please visit statsforvaltningerne.