Espinal said in the recording, "He kept saying 'Daddy punches me,' which you do when he starts crying. What do you do? You make him open up his arms, and you punch him in the chest."
Pettlon wrote in the letter, "He (Hill) categorically denies he has ever 'punched' his son in the chest or anywhere on his body, or otherwise touched him in the chest in a mean-spirited manner or as a form of discipline."
Pettlon explained there have been times when Hill has tapped his son on the chest and told him to "man up, buddy" or "don't cry, my man," but denied Hill has grabbed his son's arms as part of any discipline and further denied Hill played any part in their son suffering a broken arm. He noted the records at the hospital where the child was treated labeled the broken arm an accident.
The attorney does not deny the audio in question is of Hill and Espinal, but does challenge Espinal's assertion on the recording that the child in question is "terrified" of Hill. Pettlon also called a comment Hill made on the recording, "You need to be terrified of me, too, b----," inexcusable.
The child is not living with either parent after being removed by the Kansas Department for Children and Families last month.
Authorities have been investigating incidents -- one on March 5 for alleged child abuse and neglect, and one on March 14 for alleged battery -- at Hill's home in Overland Park, Kan. Both police reports indicated a juvenile was involved.
Kansas City Chiefs chairman and CEO Clark Hunt said Saturday that he and the front office were "deeply disturbed" by the audio, but offered no explanation as to why the team has not released him.
Speaking briefly at the team's annual draft party, Hunt said he couldn't elaborate further because of the ongoing investigation.
In November, the Chiefs moved swiftly to release running back Kareem Hunt after TMZ posted a video showing him kicking and shoving a woman in a Cleveland hotel.
The Chiefs banned Hill from participating in team activities but have not cut ties with him.
"I'd just point out that Tyreek is not with the franchise right now and we're going to go through the process," Hunt told reporters. "We'll make the right decision about Tyreek at the right time."
The NFL is said to be considering putting Hill on the commissioner's exempt list amid the ongoing criminal investigation, according to multiple reports.
The commissioner's exempt list typically isn't used during the offseason, but the league is considering making an exception in this case, per reports, which added that the NFL has the full audiotape.