  We report a search for the flavor changing neutral current (FCNC) decay of
the top quark \tZq ($q=u,c$) in \ppbar collisions at $\sqrt{s} = 1.96\tev$
using a data sample corresponding to an integrated luminosity of 1.9\invfb
collected by the CDF II detector. This decay is strongly suppressed in the
standard model (SM) and an observation of a signal at the Tevatron would be an
indication of physics beyond the SM. Using $Z+\ge4$ jet final state candidate
events, both with and without an identified bottom quark jet, we discriminate
signal from background by exploiting kinematic constraints present in FCNC
events and obtain an upper limit of $\btZq < 3.7%$ at 95% C.L.
