Measure where you want the furring strip hung. Stagger the holes in the furring strip so they aren't in a straight line in the block. This could cause a crack. Hold the furring strip up to the hole measurements to ensure it is in the right position.
Use a hammer drill with the right-size bit. Choose a bit slightly smaller than the concrete screw you are using. For example, use a 3/16 screw and a 5/32 bit. Use a carbide-tipped masonry bit.
Wrap a piece of masking tape around the drill bit to show how deep you want the hole. Determine this by measuring the length of your concrete screws. Do not drill any deeper than necessary into the block, as you might weaken it.
Drill straight into the block using the hammer drill. Work carefully, and stop when you reach the masked area on the drill bit.
Vacuum the hole to remove all of the dust.
Hold the furring strip in place and insert your screw into the hole. Turn the screw into the hole using a regular drill. Work slowly with short bursts to avoid stripping the screw.