The woman behind the suit is Kaila Crews ... who claims she was walking around the Lenox Square shopping center back in February when Broner approached her and "swiped his hand across [her] private parts."

"At no point had Plaintiff given [Broner] permission to touch any part of her body," Crews' lawsuit states.

Part of the incident was captured on video -- including the moment Broner was handcuffed by police and arrested for misdemeanor sexual battery.

Crews claims she suffered emotional distress from the incident and says Broner needs to pay up for any injuries she experienced, along with pain and suffering.

As for the criminal case, investigators are still collecting evidence.

Meanwhile, Broner has a fight scheduled for April 21 -- where he's due to face off against Jessie Vargas at the Barclays Center in Brooklyn.