Midnight Rule Relief Act of 2016 This bill prohibits a federal agency (excluding the Federal Election Commission, the Board of Governors of the Federal Reserve System, the Federal Deposit Insurance Corporation, or the U.S. Postal Service) from proposing or finalizing any midnight rule unless the Office of Information and Regulatory Affairs (OIRA) of the Office of Management and Budget finds that such a rule will not result in: (1) an annual effect on the economy of $100 million or more; (2) a major increase in costs or prices; (3) significant adverse effects on competition, employment, investment, productivity, innovation, or the ability of U.S.-based enterprises to compete internationally; or (4) a significant economic impact on a substantial number of small entities. The bill defines "midnight rule" as an agency statement of general applicability and future effect that is issued during the moratorium period, that is intended to have the force and effect of law, and that is designed to: (1) implement, interpret, or prescribe law or policy; or (2) describe the procedure or practice requirements of an agency.  The "moratorium period" begins on the day after the Tuesday next after the first Monday in November in every fourth year succeeding a presidential election and extends through January 20 of the following year in which a President is not serving a consecutive term. The bill exempts any midnight rule that the President determines is necessary: (1) because of an imminent threat to health or safety or other emergency, (2) to enforce criminal laws, (3) to protect U.S. national security, or (4) to implement an international trade agreement. The moratorium does not apply to a midnight rule if the OIRA finds that such rule is limited to repealing an existing rule and publishes a certification of that finding in the Federal Register.