  We present a search for electron neutrino appearance from accelerator
produced muon neutrinos in the K2K long baseline neutrino experiment. One
candidate event is found in the data corresponding to an exposure of 4.8*10^19
protons on target. The expected background in the absence of neutrino
oscillations is estimated to be 2.4+-0.6 events and is dominated by
mis-identification of events from neutral current pi^0 production. We exclude
the \nu_\mu to \nu_e oscillations at 90% C.L. for the effective mixing angle in
2-flavor approximation of sin^2(2theta_\mu_e) (~= 1/2 sin^2 2 th_13) > 0.15 at
Delta m^2_\mu_e = 2.8*10^{-3} eV^2, the best fit value of the \nu_\mu
disappearance analysis in K2K. The most stringent limit of sin^2(2theta_\mu_e)
< 0.09 is obtained at Delta m^2_\mu_e = 6*10^{-3} eV^2.
