The KTeV E799 experiment has conducted a search for the rare decays KL->pi0pi0mu+mu- and KL->pi0pi0X0->pi0pi0mu+mu-, where the X0 is a possible new neutral boson that was reported by the HyperCP experiment with a mass of (214.3 pm 0.5) MeV/c^{2}. We find no evidence for either decay. We obtain upper limits of Br(KL->pi0pi0X0->pi0pi0mu+mu-) < 1.0 x 10^{-10} and Br(KL->pi0pi0mu+mu-) < 9.2 x 10^{-11} at the 90% confidence level. This result rules out the pseudoscalar X0 as an explanation of the HyperCP result under the scenario that the bar{d}sX0 coupling is completely real.
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