If you are in doubt regarding if an animal has been slaughtered in a permissible manner, you cannot eat it.
'Adi b. Hatim reported:
I asked Allah's Messenger (sallallaahu alayhi wa sallam) about hunting. He said: When you shoot your arrow, recite the name of Allah, and if you find it (the arrow) killed (that). then eat, except when you find it fallen into water, for in that case you do not know whether it is water that caused its death or your arrow.
[Sahih Muslim 1929]
فِيهِ بَيَان قَاعِدَة مُهِمَّة ، وَهِيَ أَنَّهُ إِذَا حَصَلَ الشَّكّ فِي الذَّكَاة الْمُبِيحَة لِلْحَيَوَانِ لَمْ يَحِلّ ; لِأَنَّ الْأَصْل تَحْرِيمه ، وَهَذَا لَا خِلَاف فِيهِ
In it [i.e. the Hadith] is a very important principle. That is that when there is doubt regarding the permissible [method of] slaughtering of an animal then it is not permissible [to eat it]. This is because the basic principle is that the animal is impermissible to eat. And there is no difference of opinion in regards to this.