Attorney N. Trey Pettlon sent a four-page letter to the NFL, issuing a denial of the allegations made against Hill. The letter, which was obtained by ESPN, also accused Hill's fiancee, Crystal Espinal, of abusing their 3-year-old son.
Espinal secretly recorded Hill in the audio, which was aired on April 25 by KCTV in Kansas City.
Johnson County District Attorney Steve Howe declined to press charges against Hill a day before the audiotape surfaced. He has since reopened the case.
Espinal accuses Hill of abusing the boy in the audio, saying the wide receiver made the boy open his arms as Hill punched him in the chest.
Pettlon wrote that there have been occasions when Hill has "tapped his son gently on the chest" and told him to "man up, buddy" or "don't cry, my man." Pettlon wrote that Hill denies grabbing the boy's arms to discipline him.
"He 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 wrote.
Hill also denied having any role in breaking the boy's arm and a claim that his son is "terrified" of him, which Espinal said in the released audio recording.
Hill said "you need to be terrified of me, too, [expletive]" in the recording, referring to Espinal. Pettlon called that comment "inexcusable."
Hill has been barred indefinitely from Chiefs off-season team activities. The team is conducting an internal investigation into the matter.
The Chiefs wide receiver intends to cooperate with the NFL investigation "to the extent that he can under the law," the letter said.
Hill, 25, is playing on the final year of his rookie contract. He is set to make more than $2 million in 2019. Sources told NFL Network in March that the Chiefs were negotiating a new contract for the fifth-round pick in the 2016 NFL Draft. The deal was expected to be record-setting.