If you want an entire project to be non-billable, in other words all the time and expenses logged for that project to be non-billable by default (say a pro bono case), you should use the Marketing or Overhead contract type. You can later change those non-billable entries into billable, if required. Check CORE Help for details. If you want to track any fees for non-billable projects, you must create an item record and associate it with the desired income account (accounts receivable).
CORE Help Center