Police are finally revealing more about their criminal investigation into Tyreek Hill ... saying in an incident report, obtained by TMZ Sports, that they launched their probe into the NFL star after he was accused of slapping a man during an altercation on a boat.
According to the Miami-Dade Police Department docs, the incident happened at around 6:45 PM on June 18 in a Miami marina ... after Hill and some of his apparent acquaintances had boarded a fishing charter vessel without the owner's permission.
Cops say when employees of the ship found Hill's group -- they tried to kick them off ... but a verbal argument broke out instead.
During the tiff, it's alleged Hill reached out and slapped one of the employees "on the back of the neck with an open hand" as members of the 29-year-old's group tried to usher him away from the area.
Cops say Hill then "charged towards" the employee -- but he was "restrained by several people within his group."
The Dolphins receiver then left the area, cops say.
According to the docs, Hill and his group had inquired about renting the boat earlier in the day prior to the confrontation with employees -- but did not go through with the purchase "due to the high" cost.
So far, no arrests have been made ... and no charges have been filed.
Neither Hill nor his agent, Drew Rosenhaus, have yet to publicly comment on the allegations.
For the Dolphins' part, they said in a statement Tuesday they were "aware of the situation and have been in contact with Tyreek, his representatives and the NFL. We will reserve further comment at this time."