(CBS NEWS) GROVE CITY, Ohio -- A convicted sex offender released from prison in November has been charged in the shooting death of a 21-year-old Ohio State University student.

Grove City police say 29-year-old Brian Golsby was arrested early Saturday and charged with aggravated murder, kidnapping and aggravated robbery in the slaying of Reagan Tokes. Her nude body was found Thursday near a park entrance in Grove City. She was last seen leaving work at a Columbus restaurant Wednesday night and was reported missing by her off-campus roommates and co-workers when she never made it home.

Tokes grew up outside Toledo. She was a fourth-year psychology major at Ohio State and was due to graduate in May.

Grove City Police Sgt. Chris White said at a news conference Saturday that Tokes was shot twice in the head. A coroner didn’t find any other visible injuries but would be testing a rape kit, White said.

Golsby was arrested around 4 a.m. Saturday after being identified as a suspect through DNA evidence gathered in and around Tokes’ car, which was found not far from where Golsby was living in Columbus, White said. Police believe Tokes encountered Golsby not long after she left the restaurant shortly before 10 p.m. Wednesday.

Monday, Golsby was ordered held without bond. His attorney did not object, according to CBS affiliate WBNS.

The charges against Golsby also were based on statements he gave to police, White said.

Asked if Golsby had confessed, White said: “He gave us details of these events of that night that closely match what we’re finding.”

Golsby registered as a sex offender after being released from prison. He pleaded guilty in Franklin County Common Pleas Court in Columbus to aggravated robbery and attempted rape charges in May 2011 and received a six-year sentence.

Tokes’ uncle, Jeff McCrary, issued a statement on behalf of her family.

“We will always remember Reagan as a vibrant, loving young woman who embraced life,” the statement said. “She made a positive impact on people, was enthusiastic about everything and brought laughter and joy to all who knew her.”