In the Mission: Impossible series and movies, Ethan Hunt's mission briefings always end with the sentence "Your mission, should you choose to accept it, is to (...)". Has he ever used that option and refused a mission?
I am pretty sure the asker is asking about the Mission Impossible film series because there was no character named Ethan Hunt in the the TV series. Ethan hunt was the name of the IMF operative in the film series.
The films feature Tom Cruise as Ethan Hunt, an IMF agent.
And in the film series, he never refused a mission, we know that.