Mom has dementia and she told me awhile back that she took out a POA for me. How can I obtain a copy of that POA?

Ask her if she remembers where it is. She should have given it to you when she had it written. Do you know what lawyer she used? Maybe they have a copy.

If your mother has an attorney, give her a call to see if they prepared it. She might have a safety deposit box where she keeps things of this nature. Sometimes when in the hospital patients are asked to fill out medical POA forms. So think about where she would have been most likely to have encountered this form. Maybe a friend on hers would know.