Joseph Randle -- Tried to Run People Over with Car ... Cops Say

More details on the Joseph Randle arrest ... now cops say the ex-Dallas Cowboys running back was trying to run people over with his car before he was busted.

TMZ Sports broke the story ... the 24-year-old was popped Sunday morning in Kansas on 3 counts of battery, 1 count of drug possession and 1 count of criminal damage.

Now, law enforcement in Wichita says Randle tried to hit 3 people with his car -- and then tried to chase them into a home ... before forcing his way inside.

Witnesses tell TMZ Sports ... the scene was crazy -- but miraculously, no one suffered any major injuries.