Ash'ath narrates from al-Hasan (may Allah have mercy on him) that he saw no harm in a person in ihram slaughtering a bird which, if left alone, would not fly, such as the duck and the hen; and he disliked slaughtering one which, if left alone, would fly, such as the pigeon and the like.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الحج / 10030