AUSTIN, Texas -- Linda Gatica survived head injuries caused by child abuse when she was a baby, but more than three decades later they killed her in what Texas police are now calling a murder.

Yet investigators said on Thursday they aren't hunting for a suspect in the murder of Gatica, who was 36 when she died in May at an Austin care facility for people with mental disabilities.

That's because they believe the killer to be Gatica's long-dead grandmother, Martha Gatica, who abused her when she was four months old.

"Investigators learned that Linda was brought to a hospital by her mother in 1976 with head injuries that appeared suspicious," Austin police said in a statement.

Police weren't notified at the time, but Child Protective Services investigated and baby Linda was removed from her family and placed in foster care, the statement said.

'Out of the norm'
Retracing the CPS' probe, police found that the Linda Gatica's mother, Mary Jane Gatica, who was 20 at the time, had given a caseworkers differing accounts of how her daughter may have been hurt, including that she may have fallen off the bed or slipped on a toy, Austin's statesman.com reported.

Watch US News videos on NBCNews.com

Mary Jane Gatica and her three children lived with her mother at the time, the newspaper reported. 

After her death decades later, authorities concluded that the injuries suffered when she was a baby ultimately killed Linda Gatica. Further details on the injuries were not available. Police detectives decided to clear the case since the person who abused Gatica -- her grandmother -- is no longer alive.

"It's out of the norm," Austin Police Corporal Anthony Hipolito said of the case.

Reuters and NBC News staff contributed to this report. 

More content from NBCNews.com:

• Eagle Scouts return badges to protest ban on gays
• Woman charged with murder in husband's slaying outside Dunwoody day care
• College on top of Forbes' list is ...
• Study: Dispersants in Gulf could damage marine food web
• Video: RV driver backs into neighbor's pool

Follow US News from NBCNews.com on Twitter and Facebook