You have something confused. You can NOT shoot a NRA match rifle in a CMP competition.
CMP is Service Rifle only which means M1, M16A2 (or AR15), M14 (or M1A).
In NRA competitions you can shoot any rifle, but they usually divide the results in Service Rifle and Match Rifle. NRA refers to Service Rifle types being what the CMP allows, the rifles as I stated above.
There are many NRA competitions, and few CMP or Leg matches. The CMP also has the matches classified as "games", these are the M1 Garand matches and Springfield matches. Here is a link to this years CMP matches and games:
CMP