NFL investigators are working the Tyrone Crawford bar fight case -- with league officials visiting the Florida bar seeking to view surveillance video showing the Cowboys star getting physical with cops, TMZ Sports has learned. 

We broke the story ... the 29-year-old Dallas Cowboys defensive captain was involved in a massive bar brawl at the Coyote Ugly Saloon in Panama City Beach on March 15th. Multiple people were hurt in the melee. 

We know there is video showing Crawford shoving several police officers while the cops are trying to take control of the situation. Crawford has not been arrested or charged with a crime. 

But now the NFL is on the case ... we're told league investigators visited the Coyote Ugly on Tuesday hoping to view any footage which could show Crawford's involvement. 

Unclear if the bar agreed to let investigators watch the video.