Is there retaliation between a Muslim and a dhimmi?

Makhul reported: When Sayyiduna Umar (may Allah be pleased with him) came to us at Bayt al-Maqdis, Sayyiduna Ubadah bin al-Samit (may Allah be pleased with him) gave his mount to a dhimmi man to hold for him. The man refused, so he gave him a deep wound. Then he entered the mosque. When Sayyiduna Umar came out, the Nabatean cried out to Sayyiduna Umar for help. Sayyiduna Umar said: "Who is the one who hurt him?" Sayyiduna Ubadah said: "I am the one answerable for him." He asked: "What did you do to him?" He said: "I gave him my mount to hold and he refused, and I am a man with a sharp temper." He said: "Very well then, sit for retaliation." At this Sayyiduna Zayd bin Thabit (may Allah be pleased with him) said to him: "You would not have your slave take retaliation from your brother." He said: "By Allah, if I forgo the retaliation for you, I will certainly make the blood money hard on you. Pay him its blood money twice."

Ibn Abi Dhi'b said that al-Zuhri said: There is no retaliation between a Christian and a free Muslim, or a Muslim slave.