Cincinnati police has completed its investigation of the family, while federal inspectors will review the zoo.
The Hamilton County Prosecutor says the earliest he will make a decision on charges will be Friday.
Here are some questions and answers about the possible charges the parents could face:
Q: What kind of charges could the parents face?
A: Prosecutors could pursue a charge of child endangering, which makes it a crime for a parent or guardian to create "a substantial risk to the health or safety of the child by violating a duty of care, protection or support."
Q: So how likely is that to happen?
A: Legal experts think it would be very hard to prove such a charge because most child endangering cases involve parents who leave or fail to monitor a youngster for an extended period.
Q: But shouldn’t the mom have known better?
A: Again, the experts point out that the mother had been standing with the child and appeared to lose track of him for just a minute or two. They also say she didn't needlessly put the boy in danger by taking him to the zoo, and it could be argued that she surely trusted the zoo to have an enclosure that was childproof.
Q: What have the courts had to say about what constitutes child endangerment?
A: An appeals court in Ohio reversed a man's conviction for leaving a 5-year-old girl unattended on a playground near his apartment. The ruling cited other Ohio cases in which courts ruled that a mother who left her 9-year-old son in a locked car at a shopping mall and a mom who left her toddler unattended in a bathtub for 30 seconds to 4 minutes to check on another child weren't guilty of a crime.
Q: Have other parents been charged with putting a child in danger at a zoo?
A: Just a year ago, a judge sentenced an Ohio woman to probation and parenting classes after she dropped her toddler into a Cleveland zoo's cheetah pit. The woman, who authorities say dangled her 2-year-old son over a railing, initially was charged with child endangering but pleaded no contest to aggravated trespassing. The boy broke his leg.