Combating the Illicit Trade in Tobacco Products Act This bill directs the Department of State to take various actions to combat the illicit tobacco trade. The State Department shall determine whether each foreign country is a major source, point of transit, or consumer of illicit tobacco products or their precursors. If a country meets this criteria and its government is actively engaging in or knowingly profiting from the illicit tobacco trade, it shall be designated as a country of concern. If a country meets this criteria but its government is not implicated in the illicit tobacco trade, it shall be designated as a focus country. The State Department may provide focus countries with law-enforcement training and assistance to build customs and border-security capacity. The State Department may not provide development assistance or security assistance to countries of concern, with an exception for U.S. national security interests. The President may impose visa- and property-blocking sanctions on foreign persons who are responsible for or have materially assisted in the illicit tobacco trade. The President shall annually report to Congress as to sanctions imposed under this bill.