We report on a search for the flavor-changing neutral current
decays B^0_d,s -> mu^+mu^-, B^+ -> mu^+mu^- K^*0 using data from ppbar
Collisions at sqrt s = 1.8 TeV, collected with the Collider Detector at
Fermilab during the 1992-1993 running period.  We find no indication of such
decays, and we set the following 90% confidence level upper limits on
branching ratios: B(B^0 -> mu^+mu^-) < 1.6 x 10^-6, B(B^0_s -> mu^+mu^-) < 8.4
x 10^-6, B(B^+ -> mu^+mu^- K^+) < 1.0 x 10^-5, and B(B^0 -> mu^+mu^- K^*0) <
2.5 x 10^-5.