(CNN) -- Before dying, 2-year-old Riley Ann Sawyers was beaten with belts, picked up by her hair, thrown across the room and held under water, according to an affidavit from the Galveston County Sheriff's Office.
Police believe 2-year-old Riley Ann Sawyers is "Baby Grace."
The affidavit says the girl's mother, Kimberly Dawn Trenor, described to police how her daughter died and was put in a plastic storage box that Trenor and her husband, Royce Zeigler, later dumped into a Galveston waterway.
Trenor told police Zeigler tried to commit suicide the weekend before Thanksgiving, and wrote a note that said, "My wife is innocent of the sins that I committed."
The body of the then-unidentified toddler was found on October 29. A fisherman found Riley's body stuffed inside a blue storage container that washed up on an uninhabited island in Galveston's West Bay.
A medical examiner said the child's skull was fractured, and a forensic dentist estimated her age at 2 to 3 years.
Police dubbed the child "Baby Grace." A police artist's sketch of her was widely circulated in the news media and prompted a call to Galveston police from Riley's grandmother in Ohio, who had not seen the girl in months.
On Saturday, police arrested Trenor and Zeigler on charges of injuring a child and tampering with physical evidence, the sheriff's department said. Their bonds were set at $350,000 each.
The affidavit, obtained by CNN, says when police interviewed Trenor on November 23, she "gave a voluntary statement on video with her attorney present in which she describes her involvement, with Royce Zeigler, in the physical abuse, death and disposal of the remains of her daughter, Riley Ann Sawyers."
Trenor's statement said on July 24, she and Zeigler both beat the child with leather belts and held her head under water in the bathtub. She said Zeigler picked the girl up by her hair and also threw her across the room, slamming her head into the tile floor.
After her daughter died, Trenor's statement said, she and Zeigler went to a Wal-Mart that night and bought the Sterilite container, a shovel, concrete mix, and other supplies.
The statement said the box containing the child's body was hidden in a storage shed for "one to two months." Then, Trenor said, she and Zeigler carried it to the Galveston Causeway and tossed it in, and she saw it drifting away.
Riley Ann's father, Robert Sawyers, on Monday tearfully remembered her as a "fun-loving girl ... with a big imagination." Watch Riley Ann's father describe the little girl »
Riley was "very active, very hyper, but also very well-behaved," Sawyers told reporters in Mentor, Ohio.
She would play "with a water hose ... spraying the whole patio soaking wet until she was done with it," he said, as he sat behind two photographs of his daughter, a toddler with wispy blond curls.
Robert Sawyers' mother, Sheryl Sawyers, said the family was "devastated" to learn that police believe Riley is dead.
"It's hard to think that I'll never see her again," she said, clutching a red Elmo doll she had planned to give Riley for Christmas.
Maj. Ray Tuttoilmondo of the Galveston County Sheriff's Department said Monday that authorities are "fairly confident" that the toddler whose body was found on October 29 is Riley Ann Sawyers.
DNA analysis is still in progress to confirm the identification. The results will be available in two to three weeks, Tuttoilmondo said.
Tuttoilmondo said Riley is originally from Mentor, Ohio, a Cleveland suburb, and that "she and her mother came down to Texas earlier this year."
The toddler was last seen in Texas "three or four months ago," Tuttoilmondo said, although he did not know by whom.
Tuttoilmondo said police did investigate whether Child Protective Services had taken Riley away, something the mother had reportedly alleged. Of that report, Tuttoilmondo said, "What we believe is that is not what happened."
The affidavit said Trenor admitted that after the body was found, Zeigler had her type up a fake letter from the Ohio Department of Children's Services saying that Riley was to be taken away.
Trenor left Ohio in late May, after filing an allegation of domestic violence against Robert Sawyers and reaching a joint voluntary agreement that gave her custody of Riley and gave Robert Sawyers visitation rights, the Sawyers' family lawyer said Monday.
"She disappeared," Laura DePledge said Monday at the Ohio news conference with the Sawyers.
Sheryl Sawyers said Monday that she saw widely distributed police sketches of "Baby Grace" and contacted Galveston police in November. The girl in the police sketches strongly resembles photos of Riley.
"No, I never did think it would end up like this," Sheryl Sawyers said Monday, eyes welling. "I guess knowing is better than not knowing."
The girl's family in Ohio has been "very helpful" in this case, Tuttoilmondo said, adding that the FBI and a Galveston County police officer visited the family in Ohio on Sunday.
DePledge said Riley was the product of a "teenage pregnancy." Trenor and Robert Sawyers were together for two years as a result of the pregnancy, DePledge said, during which time they lived with Sheryl Sawyers.
DePledge said Monday that the family, whose grief she described as "simply overwhelming," wants Riley's body returned to Ohio for a memorial service. "What Riley needs is to be brought home," she said. "I think this family needs some closure."
Tuttoilmondo asked anyone who knew the child or her family to help detectives reconstruct the events of Riley's short life.
The toddler's case has touched even hardened police officers, he said. "Any way you look at it, we carry a piece of her with us, and we'll always carry a little piece of her with us," he said Monday.
He held up a small, pink-and-white shoe identical to those the child was wearing when she was found. "That says it all. A little-bitty shoe." E-mail to a friend
CNN's Sean Callebs contributed to this report.