Things have been bad between AB and the HPD for weeks -- with things exploding AGAIN on Monday during a domestic incident at Brown's Florida home in which Antonio cussed out and insulted officers and posted the video to social media.

The Hollywood PD says Brown's behavior was "very rude and disrespectful" and they no longer want to have a relationship with him.

As we previously reported, the HPD had allowed Brown for years to work out at their Police Athletic League football field. We posted video of AB training there in October as he tried to get back in the NFL. A spokesperson told us at the time AB had a great reputation with the cops.

In fact, cops say Brown had financially sponsored the HPD's 7-on-7 football league.

But, things have soured between the two sides ... and it's all spelled out in a new statement from the HPD detailing multiple incidents involving police where Brown treated officers terribly.

One incident took place on Dec. 14 when cops were called to AB's home for a domestic dispute involving his baby mama, Chelsie Kyriss.

"While Officers were on scene, Mr. Brown treated them with disrespect and disdain."

Cops say after the incident, they tried to contact Brown to talk things out but they couldn't get a hold of him ... so they decided to end things for good.

Ultimately, the HPD says "We made the decision to sever ties between Mr. Brown and the Hollywood Police Athletic League. We did not want our youth to be subject to this type of behavior nor emulate the actions of Mr. Brown."

Cops say they even returned AB's donation for their 7-on-7 league and have banned him from working out on their field ever again. If he returns, he could be arrested for trespassing.