Is that really the criminal courts building in Manhattan? Or a building at all in New York?

The building in the opening credits is the New York State Supreme Court Building.

Thanks nitcrt1, some good pics of it here http://images.search.yahoo.com/search/images?p=New+York+Supreme+Court&ei=UTF-8&fr=FP-tab-web-t&fl=0&x=wrt

Especially at the bottom left

This website will give you almost the view of the building as it appeared in the "Night Court" opening credits. (This is how I knew it was the same building)

http://www.nyc.gov/html/dcas/html/resources/man_supremecourt.shtml

Ha, cool. Have to get a pic taken in front of that....someday.