  We introduce $\pi$-test, a privacy-preserving algorithm for testing
statistical independence between data distributed across multiple parties. Our
algorithm relies on privately estimating the distance correlation between
datasets, a quantitative measure of independence introduced in Sz\'ekely et al.
[2007]. We establish both additive and multiplicative error bounds on the
utility of our differentially private test, which we believe will find
applications in a variety of distributed hypothesis testing settings involving
sensitive data.
