Dodgers Star Josh Beckett -- Witnesses Say Bartender's N-Word Allegation -- BOGUS

A Minnesota bartender claims L.A. Dodgers pitcher Josh Beckett hurled the N-word (with an R) at her ... but the Dodgers say they've been investigating the claim and there's NO evidence to support it ... sources connected with the team tell TMZ Sports.

The bartender says Beckett -- along with pitcher Clayton Kershaw, Orel Hershiser and 3 other Dodgers broadcasters -- were at the bar at the Grand Hotel Minneapolis on April 28th when Beckett allegedly dropped the N-bomb.

In a complaint she filed with the hotel, Mary Rohr says, "He used the N-word towards [sic] me while hanging on his teammate, Clayton Kershaw, and then asked for another cocktail," the bartender said in a letter to hotel management.

She insinuates Beckett was drunk and she was cutting him off, claiming, "I offered him a water and he began cursing at me."

Rohr says she confronted Kershaw when Beckett was in the bathroom, and he said, "Well, he's from Texas."

Sources connected with the Dodgers tell TMZ Sports ... they take any such allegation seriously and launched a full investigation, but so far her story seems "absolutely false."

We know Beckett told the team he absolutely did not use the N-word.

There are problems with Rohr's story. For starters, Clayton Kershaw was nowhere NEAR Minneapolis Monday ... we've learned he never set foot in Minnesota that day. Now we're told Rohr has changed her story and is saying the guy LOOKED like Kershaw but it was actually Dodgers pitcher Paul Maholm.

Second ... our Dodgers sources say the team has contacted Hershiser, who said, "There was no incident and Beckett never said that." We're told Rohr claims Hershiser made a beeline for the door after hearing Beckett hurl the epithet, but Hershiser told the team, "I certainly didn't make a beeline for the door. That's absolutely false."