We often connect same point of a circuit under test to several instruments if the instruments' input impedance is in the megahoms range. Is it OK to do same with several CD4051BE inputs? Meaning there are several 4051s (say 3) and the same point of circuit need connecting to those 3 chips. How to determine this using the datasheet? Or is it common knowledge based on the IC family?

Inputs referred to are marked in red, CHANNEL IN/OUT.
Datasheet at http://www.ti.com/lit/ds/schs047g/schs047g.pdf

Is there a line in the datasheet that gives the input impedance? ...assuming that is what determines the answer.

If the answer is yes/no can that be applied to all IC famillies?

 

Common knowledge... once you say the secret password.

That spec sheet tells you the Input Current is ±10-5 μA typically. So it's about... zero.

Below that it states the Input Capacitance is 5 to 7.5 pF. The cap is the killer as it needs to be charged or discharged for every change of state. Add more gates and you add more parallel caps.

Since this doesn't have digital outputs it lacks specs on how the output changes for capacitive loadings.

So... bottom line, as long as you don't mind going slower you can always add more gates. How fast you can run may need an experiment.