I need to know if the switches in the SW06 are open or closed when there is no dc supply voltage.
In general, CMOS Switches have no defined state when the power supply is not present. This means that the switch input will present a high impedance for small signals. If the input signal exceeds 0.3V then the ESD protection diodes will turn on and clip the input signal to roughly +/ 0.3V. If large signals are applied to the switch or if power is applied while a signal is being clipped, then you run the risk of putting the part into a latch-up condition, which will probably destroy the switch.
However, SW06 in particular, are by default "on" or closed when no supply is present but the ESD protection diodes and the risk of the latch-up conditions apply.