It is narrated from Umm al-Mu'minin Sayyida Aisha (may Allah be pleased with her) that some people said: O Messenger of Allah! Some people bring us meat, and we do not know whether the name of Allah was mentioned (at the time of slaughter) or not. He said: "You mention the name of Allah (say Bismillah) and eat it." And this incident was close to the time of ignorance (Jahiliyyah).
Hadith Referenceسنن دارمي / من كتاب الاضاحي / 2015
From this hadith, it is understood that it is permissible to take meat from Muslims even if it is not known whether the name of Allah was mentioned at the time of slaughter or not, because the apparent state of a Muslim gives hope that he surely would have mentioned the name of Allah. However, it is not permissible to take meat from a polytheist unless it is seen with one's own eyes that a Muslim has slaughtered it.
(Wahidi).
The slaughtered animal of the People of the Book (Ahl al-Kitab) is permissible provided it is not killed by strangulation (jhatka). The People of the Book of today are openly polytheists; therefore, caution is better.