AUSTIN (KXAN) — A search warrant reveals more information about the investigation into a woman’s body found wrapped in a tarp and buried about a foot beneath a burn pit at a Leander home.

Peter Perius, 52, is in custody on a driving without a license charge and a tamper/fabricate physical evidence with intent to impact a human corpse charge. TCSO said Thursday further charges related to the death will be added.

KXAN reached out to Perius’ attorney and will update this story when we receive a response.

On Nov. 8, TCSO identified the woman as 36-year-old Natalie Renee Pearce of Austin.

TCSO currently has custody of the car Perius was driving when he was arrested, and a search warrant dated Thursday described wanting to check it for human remains and DNA evidence, plus any fingerprints or personal property of the woman who died.

The warrant also described how a tip on Monday about a body at a home in the 23000 block of Windy Valley Road led them to find the buried body with the help of a Texas Parks and Wildlife cadaver dog.

According to the search warrant, Perius told police when questioned that he “did not kill a woman” and said he did not know why a witness “was making this story up.”

The search warrant lays out, based on witness interviews, that police believe the suspect picked up the woman in an Austin grocery store parking lot and went with her to a pawn shop on Oct. 10. Surveillance video from that shop showed a man who looked like the suspect and employees described the woman as “acting erratically,” the warrant said.

A witness also told police he had a conversation with Perius at his home Oct. 13 about a body under a tarp, the search warrant said.

The Travis County Sheriff’s Office announced Perius’ arrest Thursday after receiving a tip Monday. It is working to notify the woman’s family before releasing her name. This marks the 12th homicide TCSO has investigated this year.