DNA testing has linked an Austin man to the killing of an elderly grandmother found beaten and sexually assaulted three decades ago in her Central Texas home, authorities said Tuesday.

Steven Alan Thomas was arrested Monday and accused of capital murder in the death of 73-year-old Mildred H. McKinney, according to the Williamson County Sheriff's Office, north of Austin.

A felony complaint says Thomas's DNA was matched to evidence found on McKinney's body through a search of the federal DNA database last month. Williamson Sgt. John Foster said DNA from Thomas was obtained previously, but declined to say when or how.

Authorities later found that a fingerprint taken from the crime scene matched Thomas.

"I was actually driving in my car I didn't know if I should pull over and start jumping up and down on the side of the road or start crying," said Investigator John Foster.

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According to the complaint, Thomas denied assaulting or killing McKinney and said he did not know her. His bond has been set at $1.5 million. Williamson County jail records Tuesday did not list an attorney for him.

McKinney was found dead on Nov. 4, 1980, in her southwest Williamson County home. Authorities said she had been bound with cords, ties and pantyhose. A silver tea set, jewelry and her purse were missing.

Testing in 1999 showed there was someone else's DNA on one of the ties taken from McKinney's home. Thomas was not linked by authorities to the DNA until last month, authorities said.

Advocates for Michael Morton, the Central Texas man once convicted of killing his wife and later exonerated, once thought the deaths of Christine Morton and McKinney might be connected. The two murders occurred in homes less than a mile away from each other, though the killings were seven years apart. Both women were found in their beds and had furniture piled on them after they were killed.

DNA testing on the bandana found near the Morton home eventually produced another suspect, Mark Alan Norwood. But Norwood's DNA was not found in the evidence obtained in the McKinney case, the Austin American-Statesman reported earlier this year.

McKinney's daughter, Pat Stapleton, would later join Morton in a federal lawsuit seeking DNA testing. The case was dismissed by a federal judge who said Stapleton, as a crime victim, could not compel the state to allow her access to evidence.

"Pat Stapleton strove valiantly to focus law enforcement on her mother's murder," said John Raley, a Houston attorney who represented Morton, on Tuesday. "I hope this news will provide comfort to her family."

In a statement from Bob Stapleton, McKinney's grandson, he and his family thanked the sheriff's office for their work.

"She was a glorious woman who my family and I love and cherish and who will continue to live on in our fondest memories," Stapleton said.

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The Associated Press contributed to this report.