Dallas police say a 4-year-old boy reported missing Sunday evening was "never in any danger" -- and was never actually in his father's car when it was reported stolen. Investigators learned Fermin Fuentes was safe with his mother the entire time, as the couple is estranged.

A police spokesperson said they're now working with the Dallas County District Attorney's office exploring possible charges for the father related to making a false kidnapping claim.

Fermin's father initially told police that his son was in the backseat of his car when it was taken from the parking lot of a McDonald's near S. Buckner Boulevard and Bruton Road shortly before 6:30 p.m. Sunday.

Officers found the vehicle about three hours later in the 1800 block of Rylie Road, but the boy was not inside, police said.

Two men and a woman were taken into custody at the scene and an Amber Alert was issued for Fuentes at 10:41 p.m.

Through the course of their investigation, police said Fuentes' father "had inconsistencies in his report of the incident" -- and falsely claimed the boy's mother was in Mexico with no way to be contacted.

Investigators later learned Fermin was safe and was with his mother the entire time.

Police said Fuentes' father had not been taken into custody as of Monday evening.

Another question raised in this case is why the late night emergency phone alert was so vague. It gave no details, instead it said, "Any information regarding this abduction, call Dallas Police Department."

A DPD spokesperson said the department gave the Texas Department of Public Safety all the information and followed up with them to correct it.

"At about 10:42 p.m., DPS sent out the alert without information on the believed missing child, a description of suspects or a vehicle. We contacted DPS and they quickly added the information on their Facebook page as well as other social media sites," Dallas police wrote Monday on its blog.

Texas DPS normally sends information to the National Center for Missing and Exploited Children, who then sends the phone alert. Many people got the alert at 11:03 p.m., past the typical 11 p.m. cutoff.

NBC 5 reached out to both agencies asking for clarification on what happened, but have not yet received a reply.