This Letter describes the first determination of bounds on the CP-violation parameter 2beta(s) using B(s)(0) decays in which the flavor of the bottom meson at production is identified. The result is based on approximately 2000 B(s)(0)-->J/psiphi decays reconstructed in a 1.35 fb(-1) data sample collected with the CDF II detector using pp collisions produced at the Fermilab Tevatron. We report confidence regions in the two-dimensional space of 2beta(s) and the decay-width difference DeltaGamma. Assuming the standard model predictions of 2beta(s) and DeltaGamma, the probability of a deviation as large as the level of the observed data is 15%, corresponding to 1.5 Gaussian standard deviations.