Hello from January 2016! No CW app available on the Apple TV 4.
I've tried streaming from the CW App on my iPad Air and using AirPlay to the Apple TV, but that is hit or miss. I don't know if my AirPort just can't handle the dual jobs, but the video on the Apple TV drops out (leaving the audio) or goes to the Apple TV home screen. I can start it up again, but after a while I get aggravated and just watch on the iPad.