The production company that made "Mission Impossible" also made the original Star Trek series. That's why you often saw guest spots from actors like Leonard Nimoy on MI.
Desilu studios made both series but Leonard was not a guest star on Mission Impossible. He replaced Martin Landau when he (Martin) and Barbara Bain had a contract dispute.
Wheels
Ah ok, thanks for the clarification.
There were definitely actors from Star Trek who did guest star such as George Takei and William Shatner over the run of the series. Not in the same episode though.
