In the context of education, the issues of integrating artificial intelligence (AI) into teaching and maintaining academic integrity in students' use of AI are particularly relevant. This paper empirically examined the issue of ChatGPT usage for writing homework from the perspectives of students and professors. Study research methods included both quantitative and qualitative approaches. In Study 1, an anonymous questionnaire was administered to 350 Croatian students, users of ChatGPT, to investigate their perceptions, attitudes, habits, and intentions regarding ChatGPT usage for homework assignments. In Study 2, twelve faculty members were tested on their accuracy of distinguishing between original students' papers and ChatGPT-generated papers. For this purpose, 25 different versions of papers for 8 different courses were prepared. The results of the students' survey showed that most students still do not use ChatGPT regularly and have neutral attitudes about its usefulness, ease of use, risks, and intentions for future use. In addition, they were moderately concerned about ethical issues around its usage. Differences across gender and field of study were found. Professors, on the other hand, reported having average self-efficacy in appraising authorship, which is in line with their low average accuracy of 53%. Accuracy in distinguishing was lowest when ChatGPT was instructed to write a paper as a student. These results strongly suggest the necessity for clear guidelines, plagiarism detection tools, and educational initiatives to promote ethical use of AI technology.