  A theoretical investigation of the three-photon transition rates $
2^1P_1\rightarrow 2^1S_0\;,1^1S_0 $ and $ 2^3P_2\rightarrow 2^1S_0\;,1^1S_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.
