Detected as a problem in foreign language learning, polysemy has been a subject of many various studies and from many various aspects. The problem of polysemy is particularly important in English for Specific Purposes, or in our case English for Police Purposes, since it very often gets unnoticed by learners. Having learnt one meaning in a General English course, learners are usually unaware that the same word can have a new meaning in technical texts. The aim of the case study is to examine to what extent the students can recognize the senses of polysemous words in different contexts and if the level the particular meaning is associated with (according to the CEFR) influences the percentage of correct/incorrect answers. We used a questionnaire and a self-designed vocabulary test to collect the data both about the participants and their practical knowledge of polysemy. The study was conducted with a group of I-year students of Forensic Engineering at the University of Criminal Investigation and Police Studies. The results obtained should help improve the course of English for Police Purposes.