Kim Scott — Eminem‘s ex-wife — was overcome with emotion after officers slapped handcuffs on her … breaking down in tears during her DUI arrest.

We’ve obtained a clip of the interaction between Scott and cops … which begins with an officer asking Scott what happened — and she explains she turned a corner and was blinded by the lights of a truck, leading her to crash into another vehicle.

As Kim’s grabbing her license and registration, the officer asks her if she’s had anything to drink … and she admits she’s imbibed — but much earlier in the evening.

We broke the story … Kim was arrested last week near Detroit after cops say she hit a car. She was booked on a suspected DUI charge — with cops alleging she had a BAC twice the legal limit at the time of her arrest.

She clearly was feeling at least somewhat better later on … because she sported a big grin in her mug shot — and video from inside the precinct shows an officer telling her they’ll let her go once she sobers up and checking her BAC once again.

The arrest came just days after Kim pled no contest to charges of impaired driving and failure to report an accident stemming from a February incident where prosecutors say she hit a parked car while taking her son, Parker, and three of his friends shopping.