Infrastructure as Code (IaC) automates the creation, configuration, management, and monitoring of computing infrastructure through code. One of the key principles that IaC promises is repeatability and reproducibility. However, certain programming practices in IaC platforms, especially those that allow imperative configuration, such as Ansible, hinder reproducibility in IaC scripts. This study, first, identifies such programming practices that we refer to as reproducibility smells by conducting a comprehensive multi-vocal literature review and propose a first-ever validated catalog of reproducibility smells for IaC scripts. We implement a tool viz. REDUSE to identify reproducibility smells in Ansible scripts. Furthermore, we conduct an empirical study to reveal the proliferation of reproducibility smells in open-source projects and explore correlation and fine-grained co-occurrence relationships among them. We observe that broken dependency chain smell occurs the most in approximately 71% tasks that we analyzed. Our analysis uncovers significant positive correlations between specific reproducibility smells, implying that repositories with one such smell tend to exhibit others. Moreover, the co-occurrence analysis reveals smell pairs that show a high tendency of co-occurrence at the task granularity. With the developed tool REDUSE, DevOps engineers can identify and rectify reproducibility issues before becoming part of the production system. Software engineering researchers can use the smells catalog proposed first in this study and can utilize REDUSE in empirical studies exploring various facets of reproducibility.