What I remember from my visit to NYC in 2008 is that all tourist attractions had one police check point (metallic / bomb detectors) and the statue of liberty had it two times.

I found it quite ironic.

Edit: Another funny experience was me being stopped by security guards when I tried to take a picture of the Federal Reserve building when standing in front of it, only to be handed a brochure with on the cover a picture of pretty much the same angle.