D∗0 mesons, produced in e+e− annihilations, are observed in the γD0 and π0D0 decay modes, where the D0 subsequently decays into K−π+. The production cross section and the xE distribution for D∗0 mesons are extracted from the data, and compared with corresponding measurements for D∗+ mesons. The branching ratio for the D∗0 radiative decay is measured to be 0.53 ± 0.13. An upper limit for the σ · BR of the F∗+ meson, where the associated F+ decays into φπ+, is also derived.