Volume 4, Book 52, Number 64 :
Narrated by Anas bin Malik (radiallaahu `anhu)
Um Ar-Rubai’ bint Al-Bara’, the mother of Hartha bin Suraqa (radiallaahu `anhu), came to the Prophet (sallallaahu `alayhi wasallam) and said, “O Allah’s Prophet! Will you tell me about Hartha?” Hartha has been killed (i.e. martyred) on the day of Badr with an arrow thrown by an unidentified person. She added, “If he is in Paradise, I will be patient; otherwise, I will weep bitterly for him.” He said, “O mother of Hartha! There are gardens in Paradise and your son got the Firdaus-al-A’laa (i.e. the best place in Paradise).”
This narration does not identify the person who threw the arrow, but there are other reports (not proven either authentic or weak to my knowledge) that say it was a Muslim whose arrow got Hartha (radiallaahu `anhu) by mistake killing him.
Even if we take the first scenario, there’s still a possibility that a Muslim could’ve shot that arrow. That is why his mother was upset and wanted confirmation from the Prophet (sallallaahu `alayhi wasallam).
We could discuss the fate of the person who killed Hartha (radiallaahu `anhu) here, presuming he was a Muslim, but I believe it’s unnecessary. If the companions didn’t feel the need to do so, why should we?
And as for Hartha (radiallaahu `anhu), since his intention to set out for jihad was pure and sincere, any kind of death would have been considered martyrdom in his case. It was the same with Umm Haram (radiallaahu `anhaa), she died by merely falling off a camel, but since she was making the journey for jihad, it was considered martyrdom.