Dependencies between modules can trigger ripple effects when changes are made, making maintenance complex and costly, so minimizing these dependencies is crucial. Consequently, understanding what drives dependencies is important. One potential factor is code smells, which are symptoms in code that indicate design issues and reduce code quality. When multiple code smells interact through static dependencies, their combined impact on quality can be even more severe. While individual code smells have been widely studied, the influence of their interactions remains underexplored. In this study, we aim to investigate whether and how the distribution of static dependencies changes in the presence of code smell interactions. We conducted a dependency analysis on 116 open-source Java systems to quantify these interactions by comparing cases where code smell interactions exist and where they do not. Our results suggest that overall, code smell interactions are linked to a significant increase in total dependencies in 28 out of 36 cases, and that all code smells are associated with a consistent change direction (increase or decrease) in certain dependency types when interacting with other code smells. Consequently, this information can be used to support more accurate code smell detection and prioritization, as well as to develop more effective refactoring strategies.