To check the overflow gasket remove the overflow plate by removing the screw or screws holding the plate in place. You may need to cut away caulking from around the overflow plate before it will come off.
With the plate removed you can see what kind of shape the gasket is in. If the overflow gasket looks worn it is an easy fix to replace it. If you suspect a leak is coming from this area and the gasket is worn out replace the overflow gasket and check to see if the leak is gone.