1:30 PM PT-- The D.A. announced he hasn't spoken with either the Kansas City Chiefs or the NFL regarding the investigation.

He did say the NFL reached out, but he hadn't yet responded to their inquiry.

1:25 PM PT -- District Attorney Steve Howe, in addressing the Hill investigation, said his office is "deeply troubled by this situation and are concerned about the health and welfare of the child in question."

He added, "We believe that a crime has occurred. However, the evidence in this case does not conclusively establish who committed the crime against this child."

"Criminal cases must be proven beyond a reasonable doubt by admissible evidence, not speculation, rumor or hearsay."

Even though no charges were filed, the D.A. says there is a child protection investigation that is ongoing to make sure that the child is safe.

1:05 PM PT -- Kansas City Chiefs star Tyreek Hill and his GF, Crystal Espinal, will NOT be charged after an investigation into 2 incidents involving their child at Hill's Kansas home ... the Johnson County D.A. announced.

The D.A. is currently spelling out the details of the case as we speak ... explaining they believe a crime occurred -- but there was not enough evidence to prove who had committed the crime.

Prosecutors are set to speak about an investigation into alleged child abuse incidents at Tyreek Hill's Kansas home ... and TMZ Sports will be live streaming it all.

As we previously reported ... the Johnson County District Attorney's Office has been investigating the Chiefs star and his GF, Crystal Espinal, for weeks after police were called twice to their Overland Park, Kansas home earlier this year.

In the first incident ... cops say there was a "child abuse/neglect" situation on March 5 -- with the case report listing both Hill and Espinal as "others involved."

That case was listed as closed on March 8.

But, a separate incident report was filed just days later on March 14, listing battery involving a juvenile victim. Hill is NOT named on that report ... but Espinal was listed again as "others involved."

Prosecutors AND the Kansas Department for Children and Families both launched an investigation into the incidents ... and now prosecutors are set to speak on their findings at 1 PM PT.