GALVESTON, Texas - Authorities are trying to determine if the 2-year-old dubbed "Baby Grace" after her body was found in Galveston Bay was repeatedly abused by her mother and stepfather, an investigator said Tuesday.

A woman believed to be the mother of the girl told police she and the girl's stepfather beat and tortured the child to death, court documents show. The girl, believed to be Riley Ann Sawyers, was found by a fisherman in a plastic box Oct. 29, but her identity was unknown for weeks.

The mother told authorities how the girl died "of her own volition," sheriff's Maj. Ray Tuttoilmondo said Tuesday on CBS' "The Early Show." One of the things authorities are looking at is whether or not there was a pattern of abuse against the girl, he said.

"In a little over 20 years of doing this, I've seen a lot ... of heartbreaking cases," he said. "I think this one certainly still remains in our hearts and always will."

Investigators are awaiting DNA test results, but said Monday they are fairly confident of the girl's identity. Her mother, Kimberly Dawn Trenor, and stepfather, Royce Clyde Zeigler II, were arrested early Saturday and are in custody on charges of hurting the girl.

The details in an arrest affidavit paint a chilling picture of the girl's last days. In a statement to police included in the affidavit, Trenor, 19, said she and Zeigler, 24, killed Riley July 24.

The girl was beaten with leather belts, had her head held underwater in a bathtub and then was thrown across a room, her head slamming into a tile floor, the mother said in the document. She said they kept the body in a storage shed for one to two months before they put it in a plastic bin and dumped it into Galveston Bay.

An autopsy revealed that Riley suffered three skull fractures, but the cause of death has not been determined.

Zeigler attempted suicide last week and wrote a note saying, "My wife is innocent of the sins that I committed," according to the court documents.

Trenor said in the document that after her daughter was killed, Zeigler had her forge a document that the Ohio Department of Children's Services had taken Riley away because of allegations of sexual abuse.

Tuttoilmondo said Trenor had told relatives that someone claiming to be a social worker from Ohio, where Riley's father lives, took the girl in July. Riley's paternal grandmother, Sheryl Sawyers, hadn't seen her granddaughter in months when she saw a police sketch of "Baby Grace." Thinking it might be Riley, she called authorities in Texas.

In Mentor, Ohio, on Monday, Sawyers wiped away tears at a news conference and held up the Elmo doll she had already bought Riley for Christmas.

"It's hard to think that I'll never see her again," she said.

Trenor's attorney, Tom Stickler, said she has cooperated with authorities. He declined to comment about her statement to investigators.

"But from what she said, there is no doubt that the girl found is Riley Sawyers," Stickler said.

Trenor and Zeigler were charged with injury to a child and tampering with evidence, Tuttoilmondo said. Bail was set at $350,000 each. The couple's next court appearance was expected to be scheduled on Tuesday.

Trenor and Zeigler met a couple of years ago playing an online game, World of Warcraft, and she moved with her daughter from suburban Cleveland to Spring in June, Stickler said.

Wendell Odom, Zeigler's attorney, declined to comment on the case except to say Zeigler grew up in Spring, about 75 miles north of Galveston, and works as an instrument technician in the oil industry.

The Sawyers family's attorney, Laura DePledge, said they take comfort in knowing that the girl is "resting peacefully and is no longer subject to abuse."