"She gave a self-serving statement to investigators, which placed her with Jonathan [Foster]," Houston police spokesman Kese Smith told AOL News.
On Tuesday, the fifth-grader's badly burned body was found by a passer-by in a ditch. Evidence at the scene suggested the boy had been murdered and burned elsewhere before his body was dumped, police said.
According to the Houston Chronicle, surveillance cameras from a nearby business had recorded Nelson's image. That footage led police to her home, where they reportedly found a "boatload" of evidence, including burned carpet and twine similar to string that was found on Jonathan's hands.
Nelson, 44, was arrested at her apartment Wednesday and charged with capital murder. She was scheduled to appear in court this morning, but did not appear due to an undisclosed medical condition.
Smith said Nelson has not admitted to killing Jonathan and has offered no motive in the case.
"We're still working that aspect of it, but she has been charged with capital murder, and she is the only suspect in the case," Smith said.
A maintenance worker for several Houston apartment complexes, Nelson has a prior criminal record. In 1984, she was arrested for aggravated robbery, to which she pleaded guilty and was sentenced to 10 years' probation. Her probation was revoked in 1991, and she was sent to prison. The reason for the revocation, as well as the amount of time served, remains unclear, the Chronicle reported.
Nelson is being held without bond in the Harris County Jail.