We present a search for the decays B^)_d -> mu^+mu^- and B^0_s ->
mu^+mu^- using 17.8 pb^-1 of data collected with the Collider Detector at
Fermilab (CDF) during 1992-1993 data taking period.  We find no B^0_d
candidates in a mass window of [5.205, 5.355] GeV/c^2.  Normalizing to our
measured cross-section sigma(B^+) = 2.39 \pm 0.54 mu b for p_t(B) > 6 GeV/c
and |y(B)| < 1 and assuming sigma(B^+) = sigma(B^0_s), we find

Br(B^)_d -> mu^+ mu^-) < 1.6 x 10^-6 and Br(B^)_s -> mu^+ mu^-) < 8.4 x 10^-6

at 90% confidence level.  These limits are significant improvements of
previous measurements.