The circular dichroism in cholesteric liquid crystals (CLCs) has been studied in the absorption bands of dissolved dichroic dyes possessing both the positive and negative linear dichroism. The circular dichroism is studied depending on the position of CLC selective reflection band with respect to the dye absorption band. The induced circular dichroism due to dye absorption is compared to intrinsic CLC circular dichroism due to the light diffraction from the periodic chiral structure.