Antonio Brown not only physically assaulted a moving truck driver -- he also picked up a rock and threw it at the vehicle, causing even more damage ... this according to police.

TMZ Sports has obtained court docs in the AB alleged assault case in which the moving truck driver describes why Brown and his trainer attacked him during a routine drop-off Tuesday at Brown's Florida home.

The driver claims he was hired to deliver belongings AB had stored in California -- but when he arrived and demanded his $4,000 payment, Brown refused to hand over the cash.

The driver claims he tried to leave the home (with AB's property still in his truck) but Brown picked up a rock and threw it at the vehicle causing a dent and a paint chip on the driver's side door. The driver called police to report the vehicle damage.

A short time later, the driver was contacted by the moving company and asked him to go back to Brown's home to redeliver the goods ... telling him Brown was willing to make the initial $4,000 payment PLUS an additional $860 to cover damage to the truck and the extra work time.

Upon arrival, the driver claims AB gave him the $4,000 but refused to pay a cent more -- so again, they argued. But, this time, the driver says Brown forced his way into the driver's side of the main cabin and began to physically strike him.

Brown's associates eventually restrained the NFL star.

But, it doesn't end there ...

The driver claims AB's trainer, Glenn Holt -- a former NFL player -- grabbed the keys from the ignition and opened the side of the truck so Brown could unload his belongings.

The driver says he tried to battle Holt for the keys and suffered cuts on his hand in the process.

While AB and his pals were unloading the truck, the driver says he told the group they were taking property that belonged to another client ... so they tossed it back in the truck, causing damage to the items.

When cops eventually arrived, they found AB sitting at his front door but when he saw officers, he retreated inside and shut the door. Cops say they tried to make contact with him "with negative results."

Holt was arrested for burglary with battery. Brown was not taken into custody but sources tell us cops are working on that. Cops have said Brown is suspected of assault.

As for the driver, he claims he suffered everything from redness on his face to scratches on his neck, shoulder, stomach and forearm. He also sustained cuts on his finger.