A frightened Curran - who was crowned Miss California Regional 2016 - then called 911, accusing Brown of threatening her with a gun in a booze and drug-fuelled rage.
The model said she was not sure if she would press charges against the singer, who later surrended to police after barricaded himself inside his sprawling mansion for nine hours.
Police said at a press conference that Brown surrendered about 1pm and is co-operating with Los Angeles Police Department officers and investigators.
As police waited for a search warrant, Brown tossed a duffel bag containing at least one gun, other weapons and drugs from his window and shouted to cops "come and get me", TMZ reported.
Curran told TMZ Live she and her friend had been using Brown's hot tub before she walked back to the house.
She said one of Brown's friends was showing off a piece of jewellery.
Curran claims that when she began to admire it, the men "went nuts" before Brown pointed a gun at her and told her to "get the f*** out".
She said the Loyal singer appeared to be "on drugs or alcohol".
The beauty queen said she and her friend fled, but not before Brown's entourage demanded she sign anon-disclosure statement. She refused.
Meanwhile, the father-of-one posted a least three online videos declaring his innocence and dismissing TV reports that he was barricaded inside.
"I don't care. Y'all gonna stop playing with me like I'm the villain out here, like I'm going crazy," Brown said in one Instagram video, waving a cigarette and looking at the camera.
"When you get the warrant or whatever you need to do you're going to walk right up in here and you're going to see nothing. You idiots."