ROANOKE, Virginia (CNN) -- The family of an orphaned 3-year old girl on Wednesday agreed to genetic tests that will determine whether she was switched at birth with another newborn at a Virginia hospital in June 1995.

Rebecca Grace Chittum's grandparents, who have taken custody of her since her parents were killed in a July 4 car accident, said they believe DNA tests will confirm she is their biological grandchild.

"It's going to come back that Rebecca's going to be ours," said Tommy Rogers, Rebecca's maternal grandfather, from his home in Buena Vista, Virginia.

The grandparents initially balked at authorizing the test because they weren't sure they wanted to find out that their granddaughter is not a blood relative, said their attorney, Pete Robey.

The car crash that killed Rogers and Chittum in Buchanan, Virginia

Family members met Wednesday in Robey's office in Buena Vista -- about 40 miles northeast of Roanoke -- and agreed to authorize the DNA testing of Rebecca's blood "to bring closure to this situation," the attorney said.

Paula Johnson of Ruckersville learned last month after DNA testing for a paternity suit that Callie, the baby she took home from the University of Virginia Hospital, was not her own.

Hospital officials now believe a couple from Buena Vista -- Kevin Chittum and Tamara Whitney Rogers -- took home Ms. Johnson's baby in June 1995, while she took theirs.

Chittum and Ms. Rogers were killed in a July 4 car crash -- never knowing of the switch -- and their parents have been caring for Rebecca.

Initial tests showed Callie and Rebecca's blood types had seemingly been transposed. According to hospital records, Callie, born with the rare type O-negative, has A- positive blood, while Rebecca was born with A-positive and has O-negative blood.

Tests of DNA, the genetic code inherited from parents, prove more conclusively than blood-type tests whether or not two people are related.

The blood sample previously taken from Rebecca will be tested at a state lab in Fairfax, and the result is expected by Monday, Robey said.

Ms. Johnson said Wednesday that no matter what the blood tests show, she believes the girls should remain with the families that raised them.

"It's the only thing they've ever known," she said. "I don't see me changing my mind about taking her away from these people."

The day before, she and her former boyfriend said they hoped to work out custody and visitation arrangements with the people raising Rebecca.

University police are investigating the case as a criminal act because they believe the switch could not have been an accident, and on Monday they asked Virginia State Police to assist them.