Effect of Gate-Drain Capacitance on Input Impedance of CS Amplifier
Adding a gate-drain capacitance will add to the total capacitance seen at the gate. Including the Miller-effect, you would get something along the lines of

$$C_{in} = C_{gs} + (1-A)C_{gd}$$

The input impedance decreases because of it:

$$Z_{in} = \frac{1}{C_{in}s} = \frac{1}{(C_{gs} + (1-A)C_{gd})s}$$

It means that you will need more current to change the input voltage for all frequencies.

Note that it does not decrease the input resistance which can be considered the impedance at DC (\$s\to 0^+\$ then \$Z_{in}\to +\infty\$), which is irrelevant for MOS transistors as the gate is isolated from the channel.