  We show that ordinary and radiative muon capture impose stringent constraints
on sterile neutrino properties. In particular, we consider a sterile neutrino
with a mass between 40 to $80 {\rm MeV}$ that has a large mixing with the muon
neutrino and decays predominantly into a photon and light neutrinos due to a
large transition magnetic moment. Such a model was suggested as a possible
resolution to the puzzle presented by the results of the LSND, KARMEN, and
MiniBooNE experiments. We find that the scenario with the radiative decay to
massless neutrinos is ruled out by measurements of the radiative muon capture
rates at TRIUMF in the relevant mass range by a factor of a few in the squared
mixing angle. These constraints are complementary to those imposed by the
process of electromagnetic upscattering and de-excitation of beam neutrinos
inside the neutrino detectors induced by a large transition magnetic moment.
The latter provide stringent constraints on the size of the transitional
magnetic moment between muon, electron neutrinos and $N$. We also show that
further extension of the model with another massive neutrino in the final state
of the radiative decay may be used to bypass the constraints derived in this
work.
