The decays, <img width=119 height=32 align=center src=https://vtechworks.lib.vt.edu/bitstream/handle/10919/28846/image006.gif> and <img width=119 height=29 align=center src=https://vtechworks.lib.vt.edu/bitstream/handle/10919/28846/image008.gif> are studied using data collected at the CLEO II detector at the Cornell Electron Storage Ring. Both decays are identified using a partial reconstruction method where the <I>D<SUP>*</SUP></I> is detected only through a pion daughter from the decay <img width=64 height=25 align=center src=https://vtechworks.lib.vt.edu/bitstream/handle/10919/28846/image010.gif>. Because of the similarities in the analyses of the two modes, the ratio of the rates is measured in a way that is independent of the decay model, limited mainly by the uncertainty in the relative efficiency for detecting neutral and charged pions. This ratio is equivalent to the ratio of the product of production fraction and lifetime for charged and neutral B mesons, <img width=31 height=29 align=center src=https://vtechworks.lib.vt.edu/bitstream/handle/10919/28846/image012.gif>. It is combined with measurements of the lifetime ratio to obtain the ratio of charged and neutral B meson production at the Y(4S) resonance, <img width=175 height=29 align=center src=https://vtechworks.lib.vt.edu/bitstream/handle/10919/28846/image014.gif>.Ph. D.