Port of Lost Dreams.

A gangster's girlfriend on the run from the police, who suspect her of helping her boyfriend commit a robbery, holes up in a waterfront bar. She stows away on a fishing boat headed out to sea, and winds up falling in love with and marrying one of the fishermen, but doesn't tell him about her past. However, a year after they're married and have a child, her ex-boyfriend gets out of jail and comes looking for her.