Melissa Rycroft allegedly claimed to be the victim of a hit-and-run before cops arrested her for driving while intoxicated ... but, they say a witness totally contradicted the claim.

We've obtained a search warrant from law enforcement in Tarrant County, Texas ... which states officers responded to a call just after noon on September 23 -- where they say they found Melissa standing with an off-duty firefighter and swaying.

The officer claims Melissa had "bloodshot eyes, slurred speech" and alleges she "had a slight odor of a metabolized alcoholic beverage" on her breath. ABC

According to the docs, Melissa told an officer she'd been hit by another driver who then fled the scene ... and, the officer says he noticed damage to the right side of Rycroft's black Cadillac Escalade as we

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