Central venous catheters (CVCs) are largely used to administer chemotherapy, hemodialysis, and other treatments. Mostly made of polydimethylsiloxane (PDMS), these medical devices present an intrinsic risk of infection due to the possible formation of biofilm, thus increasing the risk of complications. Drug-releasing polymer coatings are a well-recognized strategy for combating biofilm formation. However, adhesion of the coating to the substrate over time is a major challenge. Therefore, this work aimed to design a chitosan-based coating designed to have maximum adhesion and stability to guarantee sustained drug release and antibacterial properties for at least 14 days. A coating composed of chitosan (CS) as a drug carrier, caffeic acid (CA) and copper sulphate (Cu) as crosslinkers, and moxifloxacin (Mox) as an antibiotic, was deposited through a controlled casting process onto functionalized PDMS surface. PDMS surface modification was investigated by X-ray photoelectron spectroscopy (XPS), and Fourier-transfer infrared (FTIR). Antibiotic release over time was measured in pseudo-physiological conditions (pH 7.4 and at 37 °C). Indirect cytotoxicity assays were performed on human dermal fibroblasts (HDF). The adhesion of the as-designed coating was evaluated by a specially designed pull-off test, before and after aging for 14 days in PBS. XPS and FTIR analyses confirmed the successful PDMS surface modification. The CS-CA-Cu-Mox coating resulted in being non-cytotoxic towards HDF and exhibited sustained moxifloxacin release for up to 49 days. Furthermore, the CS-CA and CS-CA-Cu coatings presented antibacterial activity for 21 days against E. coli, and for 14 days against S. aureus. Importantly, the coating maintained stable adhesion after 14 days in pseudo-physiological conditions. This study provides new insights into the adhesion behavior of polymeric coatings for medical devices, which is rarely reported in the literature.