Police say they responded to a crash just north of Lovers Lane at about 11:30 a.m. in Visalia.
When they arrived, they learned that an assault had taken place at an apartment not far from the location of the crash.
Investigators later discovered that the suspect, a 28-year-old man, who was involved in the hit-and-run, ran into the apartment complex and banged on several doors.
The victim, a 74-year-old woman, opened her door and was stabbed several times by the suspect.
She was taken to Kaweah Health for treatment but died from her injuries.
Officers located the suspect within the complex and arrested him.
While being taken into custody, the suspect tried to have officers shoot at him but failed.
The names of the suspect and victim have not been released.
The incident remains under investigation.