Kevin Garnett and his girlfriend were involved in a heated argument late last month, and cops were called to the scene ... but both sides are now saying things never got out of hand.
Law enforcement sources tell TMZ Sports ... Garnett's partner, Teare Candelier, dialed 911 just before 2 AM on April 27 to report she and Garnett had been involved in a domestic dispute at their Los Angeles-area residence.
We're told when officers arrived, Garnett had left .