Jessica McClure Morales -- the famous "Baby Jessica" who made national news when she fell down a well back in 1987 -- allegedly choked a member of her family.

According to the probable cause affidavit for Jessica's arrest ... cops in Midland County, Texas say Jessica told them the Saturday confrontation began when she and her husband got into a heated verbal argument -- during which she allegedly scratched him while trying to shove him away.

A witness apparently told the police a somewhat different story. Cops say they were told someone advised Jessica and her husband not to fight in front of a child who was in the room. Her husband allegedly said "F*** that" ... before she grabbed him by the throat.

Cops say they spoke to a witness who claims Jessica's husband shoved her away ... and that led Jessica to trip over the child.

Jessica was arrested Saturday night and charged with assault causing bodily injury involving family violence, posed for a mug shot at Midland County Jail, and was released from custody after posting bond.

You may remember ... when Jessica was just 18 months old in '87, she fell into a very narrow well at her aunt's Midland home -- becoming trapped 22 feet underground. She was finally rescued after 58 hours.