New York courts routinely apply the law of the place where the evidence in question will be introduced at trial or the location of the discovery proceeding when deciding privilege issues. However, there are circumstances where the court may undertake an interest-balancing analysis to decide whether another state's law should govern the evidentiary privilege.
Ambac Assur. Corp. v. Nomura Credit & Capital, Inc., NY Slip Op 06574 (1st Dep't September 17, 2019)
Here is the decision.