Stuntmen are widely used in many action films to shoot difficult and dangerous scenes. How is it decided whether to use a stuntman in a scene? Are there official rules for that?
I believe you are talking about stuntman/actor decision since every dangerous scene is mostly a stunt.
For minor stunts(backflips,jumps...), it is determined by director if he wants it to be real or shoot with ropes. Secondarily it is up to actor if he can do the desired trick. Sometimes actors even go through training courses just to do a good scene of a small stunt.
Major stunts with explosions,cars,... are first decided by insurance companies. You can have problems even if a stuntman gets hurt(contract). If you minimize the risk enough, the stuntman gets in action. With current CGI technologies, most scenes can now be filmed safely so it gets back to directors choice and actors capability.