[en] A search for depletion of the combined flux of active neutrino species over a 735 km baseline is reported using neutral-current interaction data recorded by the MINOS detectors in the NuMI neutrino beam. Such a depletion is not expected according to conventional interpretations of neutrino oscillation data involving the three known neutrino flavors. A depletion would be a signature of oscillations or decay to postulated noninteracting sterile neutrinos, scenarios not ruled out by existing data. From an exposure of 3.18x10²⁰ protons on target in which neutrinos of energies between ∼500 MeV and 120 GeV are produced predominantly as ν_μ, the visible energy spectrum of candidate neutral-current reactions in the MINOS far detector is reconstructed. Comparison of this spectrum to that inferred from a similarly selected near-detector sample shows that of the portion of the ν_μ flux observed to disappear in charged-current interaction data, the fraction that could be converting to a sterile state is less than 52% at 90% confidence level (C.L.). The hypothesis that active neutrinos mix with a single sterile neutrino via oscillations is tested by fitting the data to various models. In the particular four-neutrino models considered, the mixing angles θ₂₄ and θ₃₄ are constrained to be less than 11 deg. and 56 deg. at 90% C.L., respectively. The possibility that active neutrinos may decay to sterile neutrinos is also investigated. Pure neutrino decay without oscillations is ruled out at 5.4 standard deviations. For the scenario in which active neutrinos decay into sterile states concurrently with neutrino oscillations, a lower limit is established for the neutrino decay lifetime τ₃/m₃>2.1x10^-12 s/eV at 90% C.L.