Not really. They’ve got a version of the euro, called kroners, which allows Danes to believe they have their own currency. They are locked into an exchange rate band (extremely tight) which means the Danish central bank has to follow every decision the ECB takes within minutes). And this makes complete sense, in that it’s a compromise that’s edible by voters (maintaining the illusion that Denmark didn’t adopt the euro) and edible by business (allowing businesses in Denmark to participate fully in the common market).
And that’s one of the reasons Denmark has such small national debt and runs a government surplus - they can’t really invent new money because it would break the bond with the euro. So the Danish budget is sort of a “household budget” in that in contrast to, say, Sweden, they cannot create money (meaningfully) and the books have to balance (which they do; lots of oil, Novo Nordisk, Maersk, Vestas and a few other big international plays who still pay a majority of their tax in Denmark obviously helps a lot).