Caesar Syria Civilian Protection Act of 2019 This bill establishes additional sanctions and financial restrictions on institutions and individuals related to the conflict in Syria. The Department of the Treasury shall determine whether the Central Bank of Syria is a financial institution of primary money laundering concern. If so, Treasury shall impose one or more special measures, such as requiring domestic financial institutions to maintain additional records on transactions involving the bank. The President shall impose sanctions on foreign persons that (1) provide significant support or engage in a significant transaction with the Syrian government or those acting on behalf of Syria, Russia, or Iran; or (2) are knowingly responsible for serious human rights abuses against the Syrian people. The bill also imposes sanctions on those that knowingly provide various goods or services to Syria, such as aircraft for the military, technology for the government's domestic petroleum production, items on the U.S. Munitions List, and items that the President believes are being used to commit human rights abuses against the Syrian people. The sanctions include blocking of financial transactions and barring of entry into the United States. Such sanctions shall not apply to activities related to providing humanitarian aid or supporting democratic institutions in Syria. The President may suspend the sanctions under certain conditions, including if it is in the United States' national security interests. The Department of State is authorized to assist entities that are conducting criminal investigations and gathering evidence to prosecute those responsible for war crimes in Syria.