The girl's mother and stepfather remain in custody after their weekend arrest.
Galveston County sheriff's Maj. Ray Tuttoilmondo revealed little about the investigation, including how the little girl died and what role the couple might have played.
"There is still a lot more work to do," he said at a Monday morning news conference. "We still don't know the full details of what happened."
Authorities are awaiting DNA test results but believe the girl is 2-year-old Riley Ann Sawyers of the Houston suburb of Spring, 75 miles north of Galveston, Tuttoilmondo said. The girl was originally from suburban Cleveland and her father lives in Ohio.
An autopsy revealed three skull fractures, but the cause of death has not been determined.
The girl's mother, Kimberly Dawn Trenor, 19, and her husband, Royce Clyde Zeigler II, 24, were arrested early Saturday and charged with injury to a child and tampering with evidence, Tuttoilmondo said.
The couple remain jailed in lieu of $350,000 bail each. It was not immediately known who their attorneys were.
Galveston County District Attorney Kurt Sistrunk said the couple is expected to appear in court on Tuesday.
"With the investigation still ongoing, we don't know yet what additional evidence may be forthcoming. But we will certainly be guided by whatever develops when considering what additional charges, if any, will be presented to the grand jury," Sistrunk said in an e-mail.
Officials in Galveston County are working with the Harris County District Attorney's Office to determine where Riley's death occurred. Tuttoilmondo said investigators were looking at all possibilities in the case, including whether the death might have been accidental.
Tuttoilmondo said investigators became emotionally involved in determining the little girl's identity.
"Any way you look at it, we carry a piece of her with us and will always carry a little piece of her with us," he said. "She's still our little girl. She now has a family. She has people that will care for her and make sure that a box in West Galveston Bay is not where she ended her life."
A fisherman discovered the child's body Oct. 29 inside a blue plastic utility box in the bay.
Tuttoilmondo said investigators searched the couple's Spring home but he declined to say what was found or what they may have said about Riley's disappearance when they were questioned on Friday.
Tuttoilmondo did say that Trenor misled relatives when she told them that someone claiming to be an Ohio social worker took the child in July.
Attorney representing the baby's father and spokeswoman for the family
Laura DePledge told Early Show co-anchor Hannah Storm that Sawyers tried to find Riley this summer.
"We had several different reports that she was in several different states. We tried to find her throughout June, July, until the end of August. We received information at the end of august that she was in Texas," DePledge said.
A sheriff's deputy and two FBI agents visited the girl's relatives in Mentor, Ohio, Sunday to deliver the news.
Riley's paternal grandmother, Sheryl Sawyers, had called Texas authorities when she saw a sketch of the girl who had been named "Baby Grace" by authorities and thought it might be her granddaughter, Tuttoilmondo said.
Sawyers has said Riley was born to her son and Trenor while the pair were teenagers and they lived with her in Mentor, Ohio, for about two years. Trenor apparently moved with her daughter to Spring sometime this year to be with Zeigler. There apparently was a custody battle under way for Riley, officials said.
The last time Riley was seen alive was three to four months ago, Tuttoilmondo said.
The girl's grandfather, Ray Sawyers, told The Associated Press he had no comment when reached by phone Monday. He said he and other family members would attend an afternoon news conference in Mentor.
"Obviously, the family's absolutely devastated," DePledge said on CBS News' The Early Show.
Last week, authorities said the families of eight missing children from across the United States were asked to provide DNA samples. Tuttoilmondo said they were selected from 110 cases of missing children who matched a description of the girl. The child was described as being 2 or 3.
While authorities have identified "Baby Grace" as Riley, Tuttoilmondo said authorities are still looking to identify 22 other missing girls who came to their attention as a result of tips from this case.