In this short note we present results of background measurements carried out with a polystyrene based cast plastic 12.0x12.0x3.0 cm^3 size scintillator counter with a wavelength shifting fibre and a multi-pixel Geiger mode avalanche photodiode readout in the Baksan underground laboratory at a depth of 200 meters of water equivalent. The total counting rate of the scintillator counter measured at this depth and at a threshold corresponding to ~0.37 of a minimum ionizing particle is approximately 1.3 Hz.