Can a Roku box connect to an Apple TV?


Um… you can’t? You can have both connected to the same TV via different HDMI ports (or via an HDMI switch, which connects both devices to the same TV via one HDMI port on said TV, and switches between the two), but they’re both source devices, while a TV is a sink device. You can physically/electrically connect the two together, but it won’t do anything interesting.