(CNN) -- A man suspected in the slayings of his girlfriend and her four children admitted choking the Oklahoma woman to death, but said the children were not present at the time, according to an affidavit filed in the case.

Joshua Steven Durcho was arrested Tuesday after a car chase with police.

Joshua Steven Durcho, 25, was arrested Tuesday night in Hamilton County, Texas, officials said. He is suspected of killing Summer Rust, 25; her son Teagin, 4; and daughters Evynn, 3, and Autumn and Kirsten, both 7.

All five bodies were found in Rust's apartment in El Reno, Oklahoma, about 30 miles west of Oklahoma City, on Monday.

Durcho's first cousin notified authorities he found the body of Rust, who is identified in the affidavit as Summer Dawn Garas. Police also found the children's bodies in the apartment, according to the affidavit, written by a special agent with the Oklahoma State Bureau of Investigation and filed Tuesday in Canadian County, Oklahoma, District Court.

"The Medical Examiner's Office has reported to our agents that the preliminary assessment of the cause and manner of death for all five individuals was asphyxiation, suffocation and strangulation," the affidavit said. "It was also reported that each body had ligature marks around the neck. The ligature marks were also observed by OSBI crime scene investigators."

A spokeswoman for the state medical examiner's office told CNN on Wednesday that the cause of death for Summer Rust and Teagin was strangulation, and that a ligature -- which could include a string, cord or wire -- was used to strangle them. Autopsies on the three girls were being conducted Wednesday, the spokeswoman said.

A woman told police Durcho came to her apartment Monday afternoon and told her he had "choked" Summer Rust to death and that he was leaving Oklahoma, according to the affidavit. The woman asked Durcho about Rust's children, the affidavit said, and "Durcho told her that the children were at their grandmother's residence ... while he and Summer worked out their relationship problems."

The woman called Durcho's mother and told her what he had said about killing Rust, the affidavit said. Durcho's mother drove to the apartment to check on the woman, but no one answered her knocks. She then called her nephew, Durcho's cousin, to accompany her, leading to the discovery of Rust's body, according to the document.

About 6:30 p.m. Monday, the affidavit said, Durcho went to the home of another cousin, a female, and told her "he was in trouble and that he was headed out of state." Durcho was driving Rust's 1989 white Ford Thunderbird, the document said, and asked his cousin to swap cars with him, but she declined. A surveillance video showed Durcho at a truck stop on Interstate 40 about three hours later, driving the Thunderbird, the affidavit said.

Early Tuesday morning, a text message was sent from a cell phone in Durcho's possession to his mother's cell phone, according to the affidavit. Tracking and cell phone records showed Durcho's phone was located in Wichita Falls, Texas, at the time. Later that morning, Durcho called his mother, with the call shown to be from the Abilene, Texas, area, the affidavit said. Durcho's mother said "Durcho told her he loved her and had to go," according to the document.

Police said Durcho was arrested after a car chase Tuesday night. A Texas state trooper attempted to stop the car Durcho was driving because the trooper suspected the driver was drunk, according to Erin Mangrum of the Canadian County sheriff's office. When the trooper ran the license plate on the car, it matched the tag number of a vehicle sought by Oklahoma police.

The car sped off, Mangrum said, and during the ensuing chase the car crashed. Durcho suffered only minor injuries and was taken into custody, Mangrum said.

A court hearing was to be held for Durcho on Wednesday in Hamilton County, according to CNN affiliates. The Hamilton County district attorney's office did not
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Joshua Steven Durcho, 25, in Rust's apartment in El Reno, Oklahoma, Durcho came to her apartment Monday afternoon and told her he had "choked" Summer Rust to death and that he was leaving Oklahoma, according to the Joshua Steven Durcho was Joshua Steven Durcho was arrested Tuesday after a car chase with police.
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