This paper presents a novel parallel platform, C-Storm (Copula-based Storm), for the computationally complex problem of fusion of heterogeneous data streams for inference. C-Storm is designed by marrying copula-based dependence modeling for highly accurate inference and a highly-regarded parallel computing platform Storm for fast stream data processing. C-Storm has the following desirable features: 1) C-Storm offers fast inference responses. 2) C-Storm provides high inference accuracies. 3) C-Storm is a general-purpose inference platform that can support data fusion applications. 4) C-Storm is easy to use and its users do not need to know deep knowledge of Storm or copula theory. We implemented C-Storm based on Apache Storm 1.0.2 and conducted extensive experiments using a typical data fusion application. Experimental results show that C-Storm offers a significant 4.7x speedup over a commonly used sequential baseline and higher degree of parallelism leads to better performance.