I live next door to a mentally unstable woman. Do I turn over to an institution?

I recently moved into an apartment next door to a woman who is clearly mentally unbalanced.

I recently moved into an apartment next door to a woman who is clearly mentally unbalanced. She lives alone and regularly accosts me on the street. She believes I’m someone she knew from her past, and starts abusing me when I try to correct her. Other neighbours tell me she is harmless and doesn’t have a history of violence. But I believe she ought to be living in an institution equipped to look after her. What should be done?