It's somewhat unlikely they're going to become best friends or anything - she's already been rubbing him the wrong way a bit - but he doesn't just walk off, either. If she's mentally ill, it's not like it's her fault, and she hasn't been violent towards him or anything. The criminal part... well, Jim's own criminal record is mostly petty stuff - shoplifting and that sort of thing - nothing like what she's alluding to. Doesn't mean he's got to be rude and dismiss her instantly, not unless she gives him a reason to.

"I'm not gonna ask."