In this paper we report on the measurement of the rate of inclusive $pi^0$ production induced by charged-current neutrino interactions in a C$_8$H$_8$ target at a mean energy of 1.3 GeV in the K2K near detector. Out of a sample of 11,606 charged curr
ent neutrino interactions, we select 479 $pi^0$ events with two reconstructed photons. We find that the cross section for the inclusive $pi^0$ production relative to the charged-current quasi-elastic cross section is $$frac{sigma_{CCpi^0}}{sigma_{CCQE}}=0.426pm0.032(stat.)pm0.035(syst.)$$ The energy dependent cross section ratio is also measured. The results are consistent with previous experiments for exclusive channels on different targets.
