The reason that crows are linked to Pitris (spirits of departed ancestors) is described in this excerpt from the Uttara Kanda of the Ramayana. Once there was a Maheshwara Yagna (Shiva ritual) being conducted by Samvartta, brother of Brihaspati, on behalf of a king named Marutha. Since Brihaspati is the guru of the gods, the gods were in attendance. But then the demon Ravana showed up, wanting to challenge Marutha in his quest to conquer the three worlds. Ravana had famously received a boon from Brahma that made him invincible against the gods, so the gods were terrified and hid from him by changing into various animals:
And seeing that Rakshasa [demon] Ravana invincible by reason of the boon he had received, the deities, apprehensive of being worsted by him, assumed the forms of beasts. And Indra became a peacock and [Yama] the king of righteousness, a crow, and [Kubera] the bestower of riches a lizard, and Varuna a swan; and ... others also became other beasts. [emphasis added]
Then Ravana devoured (yes, devoured!) the sages present at the Yagna, and after he left the gods were grateful for the animal forms that had saved them, so they each gave a boon to the respective species of animal they had turned into. This is the boon that Yama (the god of death) gave to the crow:
Oh bird, I am well-pleased with thee. Listen to my words as I utter them. As I have been pleased with thee, thou shalt, without doubt, enjoy immunity from the various ailments to which the birds are subject. And O bird, from my curse fear of death shall not approach thee; and thou shalt exist as long as people do not slay thee. And those men residing in my dominion, being smitten with hunger, shall be refreshed along with thy relations, when thou hast eaten and been refreshed. [emphasis added]
So he gives it the boon that whenever the crows have eaten and been replenished, the Pitris (spirits of departed ancestors) will also be replenished.