  A recently reported anomaly in the time structure of signals in the KARMEN
neutrino detector suggests the decay of a new particle $x$, produced in $\pi^+
\to \mu^+ x$ with mass $m_x=33.9$ MeV. We discuss the constraints and
difficulties in interpreting $x$ as a neutrino. We show that a mainly-sterile
neutrino scenario is compatible with all laboratory constraints, within narrow
limits on the mixing parameters, although there are problems with astrophysical
and cosmological constraints. This scenario predicts that appreciable numbers
of other $x$-decay events with different origins and time structures should
also be observable in the KARMEN detector. Such $x$-decay events should also be
found in the LSND experiment and may be relevant to the search for
$\bar\nu_\mu\to\bar\nu_e$ oscillations.
