Jim Murray was a friend of Stephanie's Dad during the "good time" in Steph's life when her father went straight and got a legal paying job. Stephanie was eleven at the time. Jim would make veiled advances towards her, such as asking her if she had any boyfriends, or if she'd like to give him a fashion show. Steph was "not yet a detective" and too young to realize the signs. Once, Arthur left to force Steph's mom into rehab and left Jim to babysit Steph.
Jim grew very odd during the visit, and then he actually grabbed Stephanie. Steph immediately realized he was going to try to molest her, bit him in the face, and escaped. She hid at her school, but got scared when she heard male voices. She doubled back to her house and found Murray had gone.
When her father came back, she told him what had happened. He accused her of lying and made her never mention it again. But Steph never saw Murray again. Steph grew distrustful of men and even quit her piano lessons so she wouldn't be alone with her male teacher. She worked through those feelings though. She never called the police because her father had taught her to be distrustful of them.
On one of her first missions as Spoiler, Steph went after Jim to make sure he didn't hurt other girls. She found he had died from an overdose three days after she had told her Dad what happened.
Upon her father's death, these issues came back to Steph. She was triggered by a TV show executive talking about how a TV character who was sexually assaulted would have been "diminished" and she ended up playing piano and telling her story to Tim Drake. She still felt anger from her experience, but she was able to be calm about it and comfort a distraught Tim. She was truly upset that she would never get certain answers from her Dad: Did he kill Murray? If so, was it because he cared about Steph, or that Murray had messed with his stuff? And did Arthur have any idea what Murray was when he made him her babysitter?
She even seeked out The Riddler to get some of these answers, but he only answered in riddles.