This Letter describes the first determination of bounds on the CP-violation parameter 2βs using B0s decays in which the flavor of the bottom meson at production is identified. The result is based on approximately 2000 B0s→J/ψϕ 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 2βs and the decay-width difference ΔΓ. Assuming the standard model predictions of 2βs and ΔΓ, the probability of a deviation as large as the level of the observed data is 15%, corresponding to 1.5 Gaussian standard deviations.