This car park is a weird one. The underground portion has a closing time (which I can't recall right now), whereas the surface does not have a closing time. I feel that the way I had it tagged before worked as you could consider the upper and lower decks to be totally separate car parks with different restrictions in time and height. 

Simply having the two entrances to the lower deck tagged as "parking garage entrance/exit" could work, but as the upper and lower deck have different rules (and different signposted names which I discovered), I feel it would be appropriate to tag them as separate car parks.

Either way, I don't feel the building tag is appropriate because of the examples I mentioned previously