The Tennessee Alcoholic Beverage Commission -- the licensing authority for manufacturers, wholesalers and retailers of booze beverages in the state -- tells TMZ ... while there's no specific rule that dictates a business escorting out intoxicated patrons, let alone providing assistance to said patrons, there are laws about providing too much alcohol to someone.

We're told Tennessee law prohibits serving alcoholic beverages to someone who is visibly intoxicated -- and any violation of this is considered a class A misdemeanor.

As it pertains to claims that Riley Strain, who's still missing, was overserved ... we're told the TABC has opened an investigation to see if any violations have occurred in this matter.

Remember, it was cops who suggested Riley might've been overserved Friday when he and some friends hit the town and ended up at Luke's 32 Bridge -- where the 22-year-old was reportedly kicked out ... and where he got separated from his party and went off on his own.

As the story goes ... Riley apparently told his friends he'd meet them back at their hotel -- but he was nowhere to be found when the rest of the guys showed up. As of Thursday, there's still no sign of him ... despite an extensive search effort throughout the city.

Crews have scoured the streets, and the search for Riley has even extended to the riverbank nearby -- as some suspect he may have gotten lost and perhaps fallen into the water.

Remember, surveillance footage of Riley stumbling along the streets of Nashville has surfaced ... and he looks out of sorts, and possibly under the influence too. It's eerie video, no doubt.

Luke himself spoke out on the story, asking for prayers. He also noted his bar was cooperating with law enforcement and providing any surveillance video of their own that could help find him. We reached out to them on this latest update, but they had no comment.

Nashville PD also gave an update Thursday on where they were in the case ... noting they were scouring through tons of tips, and said they might bring in state and/or federal help if they feel they need it. For now, it sounds like it's just them handling things internally.

Riley's family has said they're living through a nightmare as they continue to look for him. Riley had apparently FaceTimed his mom earlier in the evening, and she said nothing seemed amiss then, even though they knew he was bar hopping.