Brain-computer interfaces (BCIs), based on motor imagery, are increasingly used in neurorehabilitation. However, some people cannot control BCI, predictors of this are the features of brain activity and personality traits. It is not known whether the success of BCI control is related to interhemispheric asymmetry. The study was conducted on 44 BCI-naive subjects and included one BCI session, EEG-analysis, 16PF Cattell Questionnaire, estimation of latent left-handedness, and of subjective complexity of real and imagery movements. The success of brain states recognition during imagination of left hand (LH) movement compared to the rest is higher in reserved, practical, skeptical, and not very sociable individuals. Extraversion, liveliness, and dominance are significant for the imagination of right hand (RH) movements in “pure” right-handers, and sensitivity in latent left-handers. Subjective complexity of real LH and of imagery RH movements correlates with the success of brain states recognition in the imagination of movement of LH compared to RH and depends on the level of handedness. Thus, the level of handedness is the factor influencing the success of BCI control. The data are supposed to be connected with hemispheric differences in motor control, lateralization of dopamine, and may be important for rehabilitation of patients after a stroke.