We introduce a differentially private method to measure nonlinear correlations between sensitive data hosted across two entities. We provide utility guarantees of our private estimator. Ours is the first such private estimator of nonlinear correlations, to the best of our knowledge within a multi-party setup. The important measure of nonlinear correlation we consider is distance correlation. This work has direct applications to private feature screening, private independence testing, private k-sample tests, private multi-party causal inference and private data synthesis in addition to exploratory data analysis.