I don't know about everywhere else, but if you want to shoot (pictures!) the Capital building, you'll need to get FOUR permits. There's someone (4 different people) who will sign for each of the four quadrants of the lawn - how's that for red tape, huh? Luckily they're all in the Capital building so you don't have to wander all over town - just go to some form of main office and tell them what you want to do and someone will take you downstairs.

...bring a book. ;-)

The permit(s) is(are) good for 1 week last time I checked.
Have fun and good luck-

-Lew ;-)