Output behavior of CMOS
The transfer characteristic of a CMOS inverter would look like this:

Since we are leaving the realm of digital signals, it is not a matter of which transistors are conducting, but rather how much the individual transistors are conducting. So strictly speaking, both transistors are conducting for most of the input voltage range shown in the graph. The exact voltage depends on the input voltage and the specific transistor parameters.
A state of both transistors conducting significantly is not desirable since you effectively short circuit the supply voltage. Nevertheless this state occurs for a logic transition at the input, but only for a very short time.