Google for "New Hampshire FIRST Lego League" brings up this site:
http://www.eis.na.baesystems.com/lego/index.htm
There is a webmaster link at the bottom of the page, or go to the State Tournament page and there are 3 contacts listed. I'm sure any of them could direct you.
Then you just have to go find a couple dozen judges and referees, a couple dozen more volunteers, and study what other tournaments have done to make it an enjoyable experience for teams and spectators.