Following some recent unexpected hints of neutron production in high-voltage atmospheric discharges, we present a measurement of the neutron flux in plasma discharges in electrolytic cells. We use two different types of neutron detectors, polyallyl diglycol 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 the signal previously claimed in an electrolytic cell plasma discharge experiment. Furthermore the behavior of the CR-39 is discussed to point out possible sources of spurious signals.