Cardi B told a wild story about LAPD officers searching her over suspected drug trafficking -- but it sounds like she was just yapping to yap ... 'cause there's no record of it at all.

Law enforcement sources tell TMZ ... whatever Cardi was ranting about on Monday -- namely, allegedly being detained by cops and getting strip-searched, etc. -- does not appear to be grounded in reality ... as our sources tell us there's no evidence it ever occurred.

We're told that different divisions poked around on what she was describing -- which was somewhat incoherent rambling, TBH -- simply doesn't exist on any report sheet. Our sources insist that if something as dramatic as what she described happened, it'd be documented.

Now that we know this ... it seems pretty obvious that Cardi was just BS'ing here -- something that she seemed to be telegraphing in the way she was speaking about it all.

If you didn't see it ... Cardi spun a good yarn Monday on IG Live from the comfort of her home, and it included claims of her getting stopped in her car somewhere in L.A., where she said cops suspected her of having guns and drugs on her. She then claimed she got stripped naked as cops thoroughly searched her. Like we said, it sounded like a tall tale to begin with.