Rutchey is expected to be in court again on Nov. 21 for a preliminary hearing.
An "extensive investigation" by the medical examiner revealed that the toddler died from suffocation or "some kind of airway interruption," according to a probable cause statement filed with the court.
Forensic tests determined that Eli had already been dead a week or more when law enforcement found his body. Court documents say the boy died as early as Aug. 27.
Cache County sheriff's deputies discovered the boy's death shortly after the mother went to Logan Regional Hospital seeking emergency medical treatment for herself on Sept. 4 for "a number of medical issues," according to the sheriff's office.
When hospital staff learned that she had a child, they were concerned for his well-being and sent law enforcement officers to check on him.
While at the hospital, the mother was distraught, court documents state. She called herself a "baby killer" and told hospital personnel that "something terrible has happened" and "he suffocated in the tub."
Rutchey remained hospitalized for several weeks before her arrest Thursday.
After she was taken into custody, Rutchey told officers she had suffocated her son by placing her hand over his mouth and nose, the probable cause statement states. She then tried to kill herself by overdosing on medication.