It was narrated from 'Adiyy bin Hatim that:

he asked the Messenger of Allah about hunting. He said: "When you release your dong, mention the name of Allah over him, and if you catch up with him and he has not killed (the game), then slaughter it and mention the name of Allah over it. If you catch up with him and he has killed (the game) but has not eaten any of it, then eat, for he caught it for you. If you find that the has eaten some of it, then do not eat any of it for he caught it for himself, If there are other dogs with your dog and they have killed (the game) but have not eaten any of it, then do not eat any of it, because you do not know which of them killed it."

أَخْبَرَنَا الإِمَامُ أَبُو عَبْدِ الرَّحْمَنِ النَّسَائِيُّ، بِمِصْرَ قِرَاءَةً عَلَيْهِ وَأَنَا أَسْمَعُ، عَنْ سُوَيْدِ بْنِ نَصْرٍ، قَالَ أَنْبَأَنَا عَبْدُ اللَّهِ بْنُ الْمُبَارَكِ، عَنْ عَاصِمٍ، عَنِ الشَّعْبِيِّ، عَنْ عَدِيِّ بْنِ حَاتِمٍ، أَنَّهُ سَأَلَ رَسُولَ اللَّهِ ﷺ عَنِ الصَّيْدِ فَقَالَ " إِذَا أَرْسَلْتَ كَلْبَكَ فَاذْكُرِ اسْمَ اللَّهِ عَلَيْهِ فَإِنْ أَدْرَكْتَهُ لَمْ يَقْتُلْ فَاذْبَحْ وَاذْكُرِ اسْمَ اللَّهِ عَلَيْهِ وَإِنْ أَدْرَكْتَهُ قَدْ قَتَلَ وَلَمْ يَأْكُلْ فَكُلْ فَقَدْ أَمْسَكَهُ عَلَيْكَ فَإِنْ وَجَدْتَهُ قَدْ أَكَلَ مِنْهُ فَلاَ تَطْعَمْ مِنْهُ شَيْئًا فَإِنَّمَا أَمْسَكَ عَلَى نَفْسِهِ وَإِنْ خَالَطَ كَلْبُكَ كِلاَبًا فَقَتَلْنَ فَلَمْ يَأْكُلْنَ فَلاَ تَأْكُلْ مِنْهُ شَيْئًا فَإِنَّكَ لاَ تَدْرِي أَيُّهَا قَتَلَ " .