I should perhaps expand a bit on my previous post... in general it
is a good idea to connect screens to earth, but this is largely a safety measure. If a fault provides an "unauthorised" connection between the screen and the power supply, a floating screen can be at a high voltage (depending on the voltages used) even if the fault is high resistance, and the capacitance of the cable can provide a dangerous level of shock if touched.
Obviously this isn't usually a problem at typical computer voltages, but it can be if it's used in hazardous environments (eg explosive gases present).
If it's a more serious, low resistance fault it will draw attention to the fact that something needs looking at by tripping out the power supply.