A 95-year-old woman died after a fight with another resident in her Staten Island nursing home — and cops are now probing whether it was falling or getting pushed that killed her, the NYPD said Wednesday.

Noemi Noto suffered head trauma after she hit the ground during the brawl with an 84-year-old woman at the Carmel Richmond Healthcare and Rehabilitation Center in April.

Noto was found by responding officers lying on the ground on April 9 and she was rushed to Staten Island University North Hospital, where she died from her injuries on April 17, according to police.

The medical examiner’s office ruled the incident a homicide on Tuesday, cops added.

Police are now investigating whether Noto was pushed by the other senior, or became unstable and fell during the fight.

The Staten Island District Attorney’s Office is reviewing the case for possible charges. There have been no arrests.