You still have CC reading - which means that you have organic matter in the pool. With a CYA level of zero, you want to bring up the chlorine up to at least 10ppm and test VERY frequently to bring the level back up - if you let it yo-yo the algae will grow back while the chlorine level is low.

Also - if this is an outdoor pool - the CYA of zero means that all of your chlorine will be burned off when the sun is out. You may want to add until you get to 20-30ppm of CYA (BUT make sure you check your CYA reading before adding - you don't want too much)