  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 non-interacting "sterile" neutrinos,
scenarios not ruled out by existing data. From an exposure of 3.18x10^{20}
protons on target in which neutrinos of energies between ~500 MeV and 120 GeV
are produced predominantly as nu_mu, 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 nu_mu 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 theta_{24} and theta_{34}
are constrained to be less than 11 degrees and 56 degrees 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 tau_3/m_3 >
2.1x10^{-12} s/eV at 90% C.L..
