A theoretical investigation of the three-photon transition rates 2 1 P 1 → 2 1 S 0 ,1 1 S 0 and 2 3 P 2 → 2 1 S 0 ,1 1 S 0 for the helium atom is presented. Photon energy distributions and precise values of the nonrelativistic transition rates are obtained with employment of correlated wave functions of the Hylleraas type. The possible experiments for the tests of the Bose-Einstein statistics for multiphoton systems are discussed.