Johnson County District Attorney Steve Howe acknowledged that "we believe a crime has occurred, however, the evidence in this case does not conclusively establish who committed this crime."
Police were called to the Kansas City-area home of Hill and Crystal Espinal twice last month, and investigators determined their child had been injured. Howe said the child was placed in protective care and that there will be "a continued involvement by state officials."
"I can't talk about the child, its placement or what is going on in that matter. What I can say is the child is safe," Howe said. "We want to hold people accountable that hurt children, but there are other mechanisms for us to protect that child other than filing criminal charges."
Hill released the following statement Thursday: "My son's health and happiness is my number one priority. I want to thank the Kansas City Chiefs, my attorneys, my agent and my union for supporting me through this. My focus remains on working hard to be the best person for my family and our community I can be, and the best player to help our team win."
The NFL did not respond to a request for comment on the case when asked by NFL.com.
Hill is a two-time Pro Bowl wide receiver with a history of domestic violence issues, including a case in which he was accused of punching Espinal while he was at Oklahoma State. Hill was kicked off the football team there and landed at a small school in Alabama, where he became a fifth-round pick of the Chiefs.
Hill has blossomed into one of the league's elite playmakers, and had largely stayed out of trouble until this past month, when authorities were called to his home twice in a nine-day span.
"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," said Howe, adding that the investigation took several additional weeks as he waited for police to conduct follow-up work. "One of the elements of a crime is you have to prove who that person is who committed the act."
Howe said that it was ultimately impossible to determine who injured the child.
The Associated Press contributed to this report