You could check Danbury’s tax database and see if you have any outstanding bills there, sometimes the dmv isn’t good about timely notifying towns about registration changes. If that is the case you could just give the tax collector a quick call and they will help you get the tax bill straightened out (this might be a good idea either way, they are generally pretty helpful).

And yes unfortunately everyone that owns a car has to pay the car tax, even if they are renting, since in this case the car itself is the property that they are taxing.