I'm actually a little bothered by your reference to mental illness for this person. That's frankly mine of your business, and suggestions that mental illness is the reason for this behaviour is not your role. I have witnessed similar things with culpability on both sides, so I would encourage you to consider just how you work with this individual. While you may be on separate teams, your work may have relevance to theirs, including impact on that person's performance objectives. Try to see it from all sides.

That said, the best way to deal with this isn't to ignore it. It will just compound and get worse. I suggest you discuss with your manager a facilitated discussion with said employee and management present. LR if appropriate. Explore the underlying cause and be open to working with them to find a mutually beneficial path forward.