Our mom leaves her finanances to my brother and I. She is in an assisted living facility and has dementia. Do we need to have POA?

Yes!! Contact a elder law attorney and get the ball rolling before she is considered unable to make any decisions on her own. They will be able to tell you what you need to do. Plus this has to be what mom wants too. They can write it up so right now while she can still make her own decisions she is in control but as soon as she is declared unable you can take over for her and follow her wishes. Dont wait till its too late!