Tyrese Gibson 's grandmother was detained and his house searched when cops executed a search warrant in connection to his Cane Corsos' killer behavior ... and, we now have body cam breaking down the incident.

The search went down September 22 ... and, the clip shows officers barging into Gibson's house -- marching past a big Transformers statue in the mansion's foyer.

Fulton Country Police and Animal Services look around the property, taking photos as they go ... before the clip cuts to the front of the property -- where Tyrese's grandmother has been sat in the back of a police car.

Check out the clip ... it's unclear why she's sitting the car -- but she and everyone around her seems relatively calm. No issues here. Fulton County Sheriff's Office

As we've reported ... Tyrese was a

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