Fiqh-us-Sunnah Volume 5, Hajj and ‘Umrah, Fiqh 5.060.

Abdul Malik bin Qurair reported from Mohammad bin Sirin that a man came to ‘Umar bin Al-Khattab and said: “A friend of mine and I ran after a wild game while we were in pilgrim garb. We killed a deer. What is our atonement?” ‘Umar told a man next to him: “Come, you and I must judge together.” Then he gave his verdict and told the man to sacrifice a goat in compensation.” The man left saying, “This is the Chief of the Faithful, who cannot pass a judgment concerning the killing of a deer!” ‘Umar heard the man’s remark, and he called him back and asked him: “Have you read Surah Al-Ma’idah (of the Qur’an)?” The man said: “No.” ‘Umar asked further: “Do you know this man who participated in the judgment with me?” The man said, “No.” ‘Umar said: ‘Had you told me that you have read Surah Al-Ma’idah, I would have made you ache from beating.” Then he added: “Allah, the Exalted One, says in His Book: ‘If any of you doeth so intentionally, the compensation is an offering, brought to the Ka’bah, of a domestic animal equivalent to the one he killed, as adjudged by two just men among you.’ And this man (who judged with me) is Abdur-Rahman bin ‘Awf’.”

Earlier generations of Muslim scholars gave verdicts that a camel is to be sacrificed for an ostrich, and a cow for a zebra, a stag or a deer, and similarly a sheep for a woodchuck, a pigeon, a turtledove, a mountain quail, and certain other birds. A male sheep is to be sacrificed for a hyena, a goat for a deer, a four month old goat for a rabbit, a baby goat (kid) for a fox, and a four month old goat should be sacrificed for killing a jerboa.