  Motivated by the anomalies present in $b \to s\,l^+\,l^-$ neutral current
decays, we study the corresponding $B_c \to (D_s,\,D^{\ast}_s)\mu^+\mu^-$
decays within the standard model and beyond. We use a model independent
effective theory formalism in the presence of vector and axial vector new
physics operators and study the implications of the latest global fit to the $b
\to s\,l^+\,l^-$ data on various observables for the $B_c \to
(D_s,\,D^{\ast}_s)\mu^+\mu^-$ decays. We give predictions on several
observables such as the differential branching ratio, ratio of branching
ratios, forward backward asymmetry, and the longitudinal polarization fraction
of the $D^{\ast}_s$ meson within standard model and within various new physics
scenarios. These results can be tested at the Large Hadron Collider and, in
principle, can provide complimentary information regarding new physics in $b
\to s\,l^+\,l^-$ neutral current decays.
