People would understand what you mean if you said "court", but I think "courthouse" is more correct. "Court" either refers to a wide open space that's part of a building (which I assume isn't what they mean) or the actual judicial body itself, not the building. Think orszaghaz vs. parlament.
while i agree i belive the court is used in everyday language as both building and institution. I mean people usually say "I have to go to the court" and do not need to say courthouse