In Denmark, you do not normally have to bring your registration certificate in your car.
However, you must bring Part 1 or a copy of Part 1 of the registration certificate if you drive a car which is coupled to a towing vehicle without prior inspection and approval. A towing vehicle may be a trailer, a working implement or a caravan. You must bring Part 1 or a copy of Part 1 of the registration certificate for both the car and the towing vehicle.
Abroad, you must always bring the original Part 1 of the registration certificate in your car.
You should not keep the entire registration certificate permanently in the car because when you have both Part 1 and Part 2, it is possible to re-register the vehicle to for example another owner.