  Following some recent unexpected hints of neutron production in setups like
high-voltage atmospheric discharges and plasma discharges in electrolytic
cells, we present a measurement of the neutron flux in a configuration similar
to the latter. We use two different types of neutron detectors,
poly-allyl-diglicol-carbonate (PADC, aka CR-39) tracers and Indium disks. At
95% C.L. we provide an upper limit of 1.5 neutrons cm^-2 s^-1 for the thermal
neutron flux at ~5 cm from the center of the cell. Allowing for a higher energy
neutron component the largest allowed flux is 64 neutrons cm^-2 s^-1. This
upper limit is two orders of magnitude smaller than what previously claimed in
an electrolytic cell plasma discharge experiment. Furthermore the behavior of
the CR-39 is discussed to point our possible sources of spurious signals.
