Context : Dust is expected to be ubiquitous in extrasolar planetary systems owing to the dynamical activity of minor bodies . Inner dust populations are , however , still poorly known because of the high contrast and small angular separation with respect to their host star , and yet , a proper characterisation of exozodiacal dust is mandatory for the design of future Earth-like planet imaging missions . Aims : We aim to determine the level of near-infrared exozodiacal dust emission around a sample of 42 nearby main sequence stars with spectral types ranging from A to K and to investigate its correlation with various stellar parameters and with the presence of cold dust belts . Methods : We use high-precision K-band visibilities obtained with the FLUOR interferometer on the shortest baseline of the CHARA array . The calibrated visibilities are compared with the expected visibility of the stellar photosphere to assess whether there is an additional , fully resolved circumstellar emission source . Results : Near-infrared circumstellar emission amounting to about 1 \% of the stellar flux is detected around 13 of our 42 target stars . Follow-up observations showed that one of them ( eps Cep ) is associated with a stellar companion , while another one was detected around what turned out to be a giant star ( kap CrB ) . The remaining 11 excesses found around single main sequence stars are most probably associated with hot circumstellar dust , yielding an overall occurrence rate of 28 ^ { +8 } _ { -6 } \% for our ( biased ) sample . We show that the occurrence rate of bright exozodiacal discs correlates with spectral type , K-band excesses being more frequent around A-type stars . It also correlates with the presence of detectable far-infrared excess emission in the case of solar-type stars . Conclusions : This study provides new insight into the phenomenon of bright exozodiacal discs , showing that hot dust populations are probably linked to outer dust reservoirs in the case of solar-type stars . For A-type stars , no clear conclusion can be made regarding the origin of the detected near-infrared excesses .