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Cardi B Praised by Lauren Smith-Fields' Family ... She Got Police Involved!!!

Cardi B shining light on the death of Lauren Smith-Fields helped spur a criminal investigation in Connecticut ... so says the girl's family, who is applauding the singer.

Smith-Fields' family attorney Darnell Crosland tells TMZ ... Cardi was instrumental in getting Lauren's tragic death to become a criminal case, because police launched their investigation only after Cardi spoke out.

As you know ... 23-year-old Lauren died while on a date, back in December, with a man she met on a dating app. The medical examiner announced Monday Lauren died from an accidental drug overdose, which the family questioned ... and as public pressure continued to mount, police finally said Tuesday they were opening a criminal probe.

The family's attorney says Cardi B's Sunday night tweet calling for "Justice for Lauren" -- and accusing Connecticut of failing her -- brought extra attention and made a big impact ... because there's been a ton of progress ever since.

Cardi's got an open invitation to check in with the family, in Connecticut or virtually, for an update on the investigation's progress ... and we're told Lauren's fam is overjoyed CB used her platform to speak out on behalf of their loved one.

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