The CDF experiment, which uses p(bar p) collisions at (radical)s = 1.9 TeV produced at the Fermilab Tevatron, is unique in its ability to observe all flavors of B hadrons and measure their properties. Among them, CP violation is of fundamental interest. In the B(sup +) and B(sup 0) systems, measurements of CP violation parameters performed essentially at B factories have borne out the predictions of CKM model. Little is known, experimentally, about CP violation in the B(sub s)(sup 0) system. The standard model predicts very little CP violation there, thus any nonzero measurement could be an indication of new physics. In this thesis, we will report on the very first flavor-tagged analysis of approximately 2000 B(sub s)(sup 0) (yields) J/(psi)(phi) decays reconstructed in a 1.35 fb(sup -1) data sample collected at CDF. This channel is sensitive not only to the width difference (Delta)(Lambda) in the B(sub s)(sup 0) system but also to the CP violation parameter (beta)(sub s). The final result we obtain is a confidence region in the two dimensional space of (beta)(sub s) and (Delta)(Lambda). Assuming the standard model predictions of (beta)(sub s) and (Delta)(Lambda), the probability is 15%, corresponding to 1.5 Gaussian standard deviations.