EXCLUSIVE

The woman claiming Chris Brown pulled a gun on her is wanted in NYC for questioning in connection with criminal theft ... for allegedly stealing a fancy designer purse at a swanky hotel.

The incident could be significant in the Chris Brown case, because alleged victim Baylee Curran claims a certain piece of jewelry that caught her eye triggered the events that led to her 911 call.

Baylee was vacationing with a few friends at The Plaza back in 2013 when they began arguing in the hotel. According to police docs, Baylee snatched a $1,000 Louis Vuitton purse from one of the girls and ran out of the hotel.

The purse contained $200 in cash, as well as credit cards and a Michael Kors wallet.

Security chased Baylee, who allegedly dropped the purse but somehow fled with the contents.

By the time cops arrived Baylee was long gone. There's a warrant of sorts -- it's called an I-Card -- which will allow NYPD cops to pick her up and take her to the station for questioning, if they find her in the city.

Apparently, the incident was bad enough that the alleged purse-snatching victim got a restraining order against Baylee from an L.A. judge.

Baylee's rep tells TMZ she had no idea New York City cops wanted her for questioning. She also claims her friend was the thief ... not her.

TMZ broke the story ... Baylee called 911 and accused Chris of pulling a gun on her when she says all she was doing was admiring some jewelry.