Hill said in the statement that his son's "health and happiness" are his "No. 1 priority."
Per the Associated Press (h/t NFL.com), Johnson County District Attorney Steve Howe declined to press charges against Hill or his fiancee, Crystal Espinal, and said, "We believe a crime has occurred, however, the evidence in this case does not conclusively establish who committed this crime."
Police were called to Hill's home in Kansas City suburb Overland Park twice in March, and it was determined that Hill's son was injured, which resulted in him getting placed in protective care.
In March, a source told Steve Vockrodt and Brooke Pryor of the Kansas City Star that Hill's son suffered a broken arm at their home, although no further details about how it happened were released.
Howe expressed frustration Thursday over not being able to press charges in the case: "As a prosecutor, as a father of four, yes, it frustrates me when someone hurts a child and you can't do anything about it. One of the elements of a crime is you have to prove who that person is who committed the act."
Hill pleaded guilty to domestic battery against Espinal in 2015, stemming from a 2014 assault while he was attending Oklahoma State. Hill went on to play at West Alabama and was then selected by Kansas City in the fifth round of the 2016 NFL draft.
Since entering the NFL, Hill was been one of the league's top wideouts. He is a three-time Pro Bowler as a receiver and a return man, and he is coming off a career year that saw him register 87 receptions for 1,479 yards and 12 touchdowns. He also rushed for a touchdown and returned a punt for a score.
Hill played a significant role in quarterback Patrick Mahomes being named NFL MVP in his first season as a starter.
The talented receiver is set to enter the final year of his rookie contract and will become a free agent next offseason if the Chiefs do not sign him to an extension.