Hamilton County Prosecutor Joseph Deters said once the police inquiry had finished "they will confer with our office on possible criminal charges".
The zoo says it had no choice but to kill the gorilla, and has defended its safety measures around the enclosure.
Animal activists have accused the zoo of negligence.
Stop Animal Exploitation Now, a Cincinnati-based animal rights group, said it had filed a federal complaint against the zoo with the US Department of Agriculture (USDA).
The parents of the boy, who suffered minor injuries in the incident, have also faced heavy criticism social media.
Cincinnati Police on Tuesday corrected earlier statements which had given the boy's age as four.
The police said that their review of the incident "is only regarding the actions of the parents/family that led up to the incident and not related to the operation or safety of the Cincinnati Zoo."
The case report provided by police states that witnesses said the gorilla at first appeared to be protecting the boy, but then grew agitated due to screaming onlookers. It then began to drag him.
The child fell into the enclosure of 17-year-old Harambe, an endangered western lowland gorilla, on Saturday.
Video footage showed the boy being dragged through shallow water by the animal. Zookeepers shot Harambe soon after.
The zoo on Monday defended its actions, saying it had no choice but to shoot the gorilla as tranquilisers would not have worked in time to save the boy.
It also said its Gorilla World exhibit was safe and exceeded required protocols.
But Michael Budkie, of Stop Animal Exploitation Now, said the USDA should fine the zoo for having an exhibit that the public could access.
"What happened this weekend made it very clear that the physical barriers at the Cincinnati Zoo are not adequate to keep people out of the enclosures, obviously," he said, adding that the enclosure was reported to be over 30 years old.
He also said the zoo had been criticised back in March after two polar bears were able to wander out of their pen into a service hallway.
Michelle Gregg, the mother of the boy who fell into a gorilla enclosure, has become the victim of online abuse.
People were quick to take to social media after zoo officials defended the decision to shoot the animal.
Eddie Whrnbrg wrote on Facebook: "...the zoos aren't the problem. It's the idiotic parents."
On Twitter @blxxm83 wrote: "So lazy parents can't control their wild kids and a beautiful endangered animal gets shot and killed because of it? #Harambe #RIPHarambe"
In another tweet @brittrosenthal wrote "Sad thing is it looked like #Harambe was protecting the kid more than the parent was. #CincinnatiZoo"
Some even called for Ms Gregg to be dismissed from her job.
Ms Gregg, posting on Facebook after the incident, said her son was "able to walk away with a concussion and a few scrapes... no broken bones or internal injuries".
She also had this to say to her critics: As a society we are quick to judge how a parent could take their eyes of of their child and if anyone knows me I keep a tight watch on my kids. Accidents happen but I am thankful people were in the right place today."
Her Facebook page has since been deleted.
About the same time as she made her comments, a Facebook group called Justice for Harambe was set up.
An online petition signed by more than 300,000 people was also created, calling for her to be held accountable for Harambe's death.