We present novel, low-cost and non-invasive potential diagnostic biomarkers of schizophrenia. They are based on the 'mirrorgame', a coordination task in which two partners are asked to mimic each other's hand movements. In particular, we use the patient's solo movement, recorded in the absence of a partner, and motion recorded during interaction with an artificial agent, a computer avatar or a humanoid robot. In order to discriminate between the patients and controls, we employ statistical learning techniques, which we apply to nonverbal synchrony and neuromotor features derived from the participants' movement data. The proposed classifier has 93% accuracy and 100% specificity. Our results provide evidence that statistical learning techniques, nonverbal movement coordination and neuromotor characteristics could form the foundation of decision support tools aiding clinicians in cases of diagnostic uncertainty.