Ryouko no Shinrei Jikenbo (1987)

After burying the corpse of her pet cat Pou, high school girl Ryoko Midorikawa starts seeing things unseen by others and experience poltergeistic accidents. One day, a cat strikingly resembles Pou appeared in front of Ryoko’s house, and after taking it in it soon starts talking to Ryoko telepathically, revealing himself as a spirit of a handsome young man "borrowing" Pou’s body. He has lost memories of his name and much of his personal details but there’s one thing certain: his body is inanimate but still alive, thus he needs Ryoko to find his body to return to, with more than just a few evil spirits attracted by Ryoko’s newly gained psionic abilities in their way.

Source: www.anisearch.com/manga/4930