(CNN) -- A 15-year-old South Carolina girl who was shot earlier this week by a man authorities say fits the description of a serial killer has died, police said Saturday.

"Let me say that under the FBI's definition of a serial killer, yes, we have a serial killer," Sheriff Bill Blanton told reporters in Gaffney, a town in the county of about 54,000 residents some 50 miles southwest of Charlotte.

He would not detail what has led investigators to conclude the shootings are linked

The first shooting happened Saturday, when peach farmer Kline W. Cash, 63, was found dead by his wife

Cash's home may have been robbed.

On Wednesday, the bound and shot bodies of 83-year-old Hazel Linder and her 50-year-old daughter, Gena Linder Parker, were found in the mother's home

We're dealing with a man that's killed four people."

He urged residents to check on relatives, especially those who live alone. "We're asking the people in our community to be vigilant, to report anything."