You would have to make sure, that the 2 supplies are isolated. If the 2 supplies are somehow connected to the mains, as some types of PSUs are, you could blow something up (there is something about an oscilloscope blowing up in one of Dave's videos).
If they are both isolated, you could connect the ground.
Or, to be absolutely on the safe side, you could use optical isolators. They basically take the output of one µC and drive an LED. The input of the other µC is connected to the phototransistor, which switches when the LED lights up. The two controllers are isolated and you don't have to worry about one shorting out or overloading the other.