WATCH: Father of Murdered Texas Lesbian Arrested

Police believe the 24-year-old lesbian couple found dead in Galveston, Texas, last week, may have been killed inside the home of one of the women's fathers, according to a breaking news report from Houston's KTRK. 

James Larry Cosby was arrested Thursday in connection with the death of his daughter, Britney Cosby, and her girlfriend, Crystal Jackson, both 24. The elder Cosby has been charged with two counts of tampering with evidence in relation to the double homicide. 

Galveston County investigators told KTRK they interrogated Cosby after he attended a Wednesday night vigil for the two women, which led them to search the south Houston-area he shared with the couple. 

"His house was a secondary crime scene, from the evidence that we saw when we went to interview him," Galveston County Sheriff Henry Trochesset told KTRK. "And we did recover certain parts of evidence that are here at our sheriff's office now to be sent to the lab."

When the bodies of the couple were first discovered early last Friday behind a grocery story dumpster, police said they believed the women had been killed elsewhere, with someone then moving their bodies. 

While investigators aren't yet saying if they believe the Cosby killed his daughter and his girlfriend, who had a five-year-old daughter, they did tell KTRK that the charges could be upgraded to capital murder. 

Cosby is currently in jail on a $500,000 bond, and KTRK reports that he's a convicted sex offender who was released from prison in October. His past arrests include "several assaults and weapons charges," according to the local ABC affiliate. 

Watch KTRK's report below.