It is not permissible to give zakat to a dhimmi; for Ibn Abbas, may Allah be pleased with him, said that the Prophet, peace be upon him, told Mu'adh: "Inform them that Allah has made it obligatory for them to give charity, which is taken from their rich and returned to their poor," in Sahih al-Bukhari 4: 1580, so it is restricted to the poor among Muslims.