We investigate the matching algorithm used by the German central clearinghouse for university admissions (ZVS) in medicine and related subjects. This mechanism consists of three procedures based on final grades from school ("Abiturbestenverfahren", "Auswahlverfahren der Hochschulen") and on waiting time ("Wartezeitverfahren"). While these procedures differ in the criteria applied for admission they all make use of priority matching. In priority matching schemes, it is not a dominant strategy for students to submit their true preferences. Thus, strategic behaviour is expected. Using the full data set of applicants, we are able to detect some amount of strategic behaviour which can lead to inefficient matching. Alternative ways to organize the market are briefly discussed.