The CDF Collaboration has adapted several heavy flavor tagging
techniques and employed them in analyses of time-dependent flavor asymmetries
using data from the Tevatron Run I.  The tagging algorithms were calibrated
using low-P_t inclusive lepton and dilepton trigger data samples.  The tagging
techniques were applied to a sample of \sim 400 B^0_d/B-bar^0_d -> J/psi K^0_s
decays and were used to measure the CP violation parameter, sin(2 Beta).
Prospects for future improved measurements of the CP violation parameters at
the Tevatron are briefly discussed.