(1) Background: Both patient and occupational safety cultures should be considered when promoting safety culture. To our knowledge, there are no studies that capture patient safety culture (PSC) and occupational safety culture (OSC) in hospitals while using a common questionnaire. The aim of this feasibility study in a German university hospital was to develop a questionnaire to assess both issues analogously. In addition to feasibility outcomes, we report results of PSC-OSC comparisons. (2) Methods: To assess PSC, we used the existing Hospital Survey on Patient Safety Culture (HSPSC) questionnaire. Developing new OSC “twin items” for certain parts of the HSPSC was supported by a previous literature review. Additionally, we developed multiple choice questions to examine knowledge and competencies regarding specific PS/OS aspects. (3) Results: Developing and implementing a combined PSC and OSC assessment instrument was feasible. The overall response rate was 33% (407 nurses, 140 physicians). In general, the statistical reliability of almost all scales was sufficient. Positive PSC perceptions (agreement rates 46–87%) were found in 16 out of 18 scales. Of the four twin scales, the PSC values were significantly better. Individual PS- and OS-related knowledge and competencies were lower than expected. (4) Conclusion: The comparative investigation of patient and occupational safety in a large hospital is a promising approach and can be recommended for further studies. We used our experiences that are presented here in an ongoing bicentric study on the associations between working conditions, occupational safety culture, patient safety culture, and patient safety outcomes (WorkSafeMed).