  Results on a search for pair production of second generation scalar
leptoquark in $p \bar{p}$ collisions at $\sqrt{s}$=1.96 TeV are reported. The
data analyzed were collected by the CDF detector during the 2002-2003 Tevatron
Run II and correspond to an integrated luminosity of 198 pb$^{-1}$. Leptoquarks
(LQ) are sought through their decay into (charged) leptons and quarks, with
final state signatures represented by two muons and jets and one muon, large
transverse missing energy and jets. We observe no evidence for $LQ$ production
and derive 95% C.L. upper limits on the $LQ$ production cross sections as well
as lower limits on their mass as a function of $\beta$, where $\beta$ is the
branching fraction for $LQ \to \mu q$.
