We search for dimuon decays of a low mass particle in the decays B0→K*0 X and B0→ρ0 X using a data sample of 657×10(6)BB events collected with the Belle detector at the KEKB asymmetric-energy e+ e- collider. We find no evidence for such a particle in the mass range from 212 MeV/c2 to 300 MeV/c2 for lifetimes below 10(-12) s, and set upper limits on its branching fractions. In particular, we search for a particle with a mass of 214.3 MeV/c2 reported by the HyperCP experiment, and obtain upper limits on the products B(B0→K*0 X)×B(X→μ+ μ- )<2.26(2.27)×10(-8) and B(B0→ρ0 X)×B(X→μ+ μ-)<1.73(1.73)×10(-8) at 90% C.L. for a scalar (vector) X particle.