Combination Product Regulatory Fairness Act of 2016 This bill amends the Federal Food, Drug, and Cosmetic Act to require the Food and Drug Administration (FDA) to provide the sponsor of a product the scientific rationale supporting a determination that the product is not a medical device before making that determination. If the FDA preliminarily determines that a product is not a medical device, the sponsor may propose a study to inform the product's classification. The FDA is prohibited from determining that a combination product (a product that is a combination of drug, device, or biological product) is a drug solely because the product has a chemical action. The FDA must provide the scientific rationale for deciding the primary mode of action (the most important therapeutic action) of a combination product if the FDA's decision disagrees with the conclusions of the product sponsor. (Combination products are regulated based on their primary mode of action.) The sponsor of a combination product and the FDA may agree to a combination product review plan regarding the standards and requirements applicable to the product's premarket review, postmarket modification, or manufacturing. The FDA may allow the sponsor of a combination product that contains an approved constituent product to omit information from the combination product application that is duplicative of information submitted regarding the approved constituent part. The FDA must describe the responsibilities of each agency center regarding review of combination products. The FDA's Office of Combination Products must resolve disputes regarding the premarket review of combination products within 90 days and annually report on disputes and meetings.