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We report the results of a multi-epoch survey of water maser observations at 22.2 GHz with the Medicina radiotelescope from 44 bright rimmed clouds (BRCs) of the northern hemisphere identified by Sugitani et al. (1989, ApJ, 342, L87) as potential sites of star formation. The data span 16 years of observations and allow to draw conclusions about the maser detection rate in this class of objects. In spite of the relatively high far-infrared luminosities of the embedded sources ($L_{\rm FIR}\ga 10^2$ $L_\odot$), H2O maser emission was detected towards three globules only. Since the occurrence of water masers is higher towards bright IRAS sources, the lack of frequent H2O maser emission is somewhat surprising if the suggestion of induced intermediate- and high-mass star formation within these globules is correct. The maser properties of two BRCs are characteristic of exciting sources of low-mass, while the last one (BRC 38) is consistent with an intermediate-mass object. We argue that most BRCs host young stellar objects of low-luminosity, likely in an evolutionary phase later than the protostellar Class 0 sources, and that a significant contribution to the observd IRAS luminosity comes from warm dust heated by the radiation from the bright rim