No Safe Haven in Cuba Act - Amends the Cuban Liberty and Democratic Solidarity (LIBERTAD) Act of 1996 to require, in order to determine that a democratically elected government exists in Cuba, the Cuban Government to prove its respect for the democratic rule of law by ceasing to provide a safe harbor to individuals who have been legally indicted or convicted of serious criminal offenses, including individuals who have fled from the United States to Cuba for the sole purpose of avoiding prosecution or confinement.