Can electricity pass through glass ?

I would imagine so, there's no 'perfect' insulator, and 3mm isn't terribly thick.

Edit: A quick google finds this:


A bit scary though that it specifies an inch thick, not just 3mm

An insulator is essentially a dielectric... two plates on either side of a dielectric form a capacitor. AC passes through a capacitor. So even those rubber sole shoes won't save you if the voltage is large enough and it's AC. Even if the DC is high enough it can punch through the dielectric.