Differential distributions in the $pi_0pi_0gamma$ system created in the annihilation channel of an electron-positron collision are considered. The energy fractions of the pions (Dalitz-plot) distribution are presented in a general form and in approxi
mation of intermediate vector mesons (excited and ordinary ones).It is pointed out that in relevant experiments the generalized polarizability of the neutral pion can be measured. Numerical illustrations are presented.