The MiniBooNE Collaboration reports a search for nu(mu) and nu(mu) disappearance in the Delta m(2) region of 0.5-40 eV(2). These measurements are important for constraining models with extra types of neutrinos, extra dimensions, and CPT violation. Fits to the shape of the nu(mu) and nu(mu) energy spectra reveal no evidence for disappearance at the 90% confidence level (C.L.) in either mode. The test of nu(mu) disappearance probes a region below Delta m(2)=40 eV(2) never explored before.