If you are referring to the NFHS policy which is summarized here:
https://www.nfhs.org/who-we-are/memb...als-coverages/
I don't believe it matters what sport you are "registered" as an official. It only matters that the sport in which the injury/liability occurs is recognized by your state association. So, if you are a softball umpire who works a chain crew for your local football team in the fall and you get hit in the face by Jon Moxon trying to kill the clock, your injuries should be covered if your state's HSAA recognizes football as a sport.
Also of interest...I believe this policy covers any level of sport, except semi-pro/pro. So, if you are sued for something that happens in an 8U game, NCAA, or a local beer league, you should be covered.
(I am not a lawyer, actuary, insurance adjuster, etc, etc. Read the fine print. yadda yadda.)