If you don’t have a written lease agreement, the rules of the Danish Rent Act apply without reservation. So, in this case you must find the answer to what rights you have as a tenant in the Act. The fact that there is no written agreement does not mean that you are in a worse position than what I stated in the Act – the rules on, for example, notice periods etc. apply.
Both landlord and tenant can demand a written agreement, but there are no immediate sanctions if the other party refuses. If not getting a written agreement leads to a loss, you can claim compensation.