Is this stalking or just a bad breakup?

My best friend recently ended a relationship that lasted nearly two years. His ex has always suffered from a need to control him, unfounded paranoia about his female friends (especially me), habitual lying, constant snooping, hacked into his online accounts and is a serious drama queen. The night they broke up, she called his phone half a dozen times, plus text messaged him at least twice that often. He replied politely the first few times, but then ignored her. Thursday night, less than a week after their breakup, she called him at 2 am, drunk and claiming to have been d. He told her that she needed to call the cops, not him, but she proceeded to tell him the story anyway, and once she did, he didn't believe her. Remember, she has a long-standing habit of making up stories to fulfill her need for attention, and her story was completely implausible. So, when she'd finished, he told her again to go to the hospital and call the police, but to leave him alone. Two hours later, despite frigid temps and horrible snow, she showed up at his house, still drunk and let herself in. Long story short, asking her to leave didn't work. Telling her to leave didn't work. Calling the police SEEMED to work until he hung up the phone, but then she came back. The police came, eventually, after he finally got her to leave, and he filed the report, but she had the nerve to call ask him if she could visit his (not their) five-year-old son this weekend. And when he told her no, she couldn't understand why! If it makes any difference, he's 27, she's 22. It's not like this is teenage first love or anything. I'm a little worried about him, but I don't want to overreact either. I mean, I'm a woman, but if any of my exes had done anything like that, I'd be really freaked out!