A search for new neutral scalar bosons S0 in the process e+e- -> S0Z0 is described, using data collected by the OPAL detector at center-of-mass energies of 91 GeV and 183-209 GeV. The data collected at these energies correspond to an integrated luminosity of approximately 770 pb^-1. The searches are independent of the decay modes of the S0, and the results can therefore be interpreted in various models. Since no indication for new scalar bosons was found in the data, upper limits on the cross section for the signal process have been calculated for several possible scenarios, particularly for the case that the S0 is a Higgs boson: the production of a single new scalar particle with small decay width and two scenarios which lead to a broad signal mass continuum due to numerous Higgs states or a Higgs boson with a large decay width.