Sharon Stone Says Cops Came To Protect Her During O.J. Simpson Chase

Sharon Stone didn't have any connection to O.J. Simpson back in 1994 ... but when The Juice was loose, Stone was locked up tight -- with cops sequestering her in a hotel room.

The megastar actress talked about how her fame exploded after the 1992 film "Basic Instinct" came out in an interview with InStyle Magazine ... and said she was so big two years later that when O.J. took cops on a low-speed chase, LAPD officers showed up at her door.

According to SS ... while the dramatic pursuit was in progress, officers showed up at Sharon's door and told her to pack a bag in the next 10 minutes.

Stone says one officer specifically told her, "He’s dangerous. And we don’t know how dangerous, and we don’t know what this is."

Worth noting ... Stone had no actual connection to Simpson -- leading some to wonder why the police would show up to her house anyway. Obviously, Stone was one of the biggest movie stars of the time, but tons of famous people live in L.A., and LAPD didn't go to all their houses as far as we know.

One person who didn't question why the police were there ... Sharon Stone, who quickly packed a bag and left with officers who took her to a hotel. Sharon said her life had become so crazy after "Basic Instinct" blew up she didn't think anything of the protection.

They recommended she buy a house with a gate and hire some security -- advice Stone took, and one of many expensive measures Sharon said she paid for to keep herself safe.

Of course, Simpson later returned to his home where -- following a lengthy standoff -- O.J. turned himself in to police. He was charged with the murders of Nicole Brown Simpson and Ron Goldman ... but, of course, he was found not guilty of both slayings.