  We have studied the e+e- -> omegapi0 cross section in the sqrt(s) interval
1000-1030 MeV using the pi+pi-pi0pi0 and pi0pi0gamma final states with a sample
of ~600 pb^-1 collected with the KLOE detector at DAFNE. By fitting the
observed interference pattern around M_phi for both final states, we extract
the ratio of the decay widths Gamma(omega->pi0gamma)/Gamma(omega->pi+pi-pi0) =
0.0897 +- 0.0016 and derive the branching fractions BR(omega -> pi+pi-pi0)=
(90.24 +- 0.19)%, BR(omega -> pi0gamma) = (8.09 +- 0.14)%. The parameters
describing the e+e- -> omegapi0 reaction around M_\phi are also used to extract
the branching fraction for the OZI and G-parity violating phi -> omegapi0
decay: BR(phi->omegapi0) = (4.4 +- 0.6)x10^-5.
