Calling the police on a demented little old lady (LOL) is nutsville, and is far worse than the behavior exhibited by the LOL.
To call the police, there should be a real threat. Police often arrest people, or worse. Who could a LOL harm anyway? Answer, nobody. Once I ran off a burglar with an assault rifle while getting ready to go on my first date with my future wife; however, I did not call the police, as there was no threat.
Nevertheless, it is appropriate to pause and consider what to do when unusual, challenging, or stressful events occur as the OP is doing. A better perspective than focusing on the pathetic old lady, is to consider whether God is trying to teach someone something, or else prevent something worse than an encounter with a rude person.
For example, the old lady reminded the OP that she does not lock her door. What if God, who can see the future, could see that a real intruder is planning to test the doors in the complex one by one, a week from now, and break into any open unit? If that is the case, then the old lady may have saved the OP’s property, family, or life.
One of the first things I try to think about when encountering difficult people is to consider whether I am looking at a “mirror” of something in myself. If I encounter a rude person, was I rude to someone else etc.?
Another way of looking at the experience is that the old lady is a training exercise. It is easy to be a saint with your own peer group of like minded people. It is not so easy with a difficult person. When I fall short in charity with a difficult person, I equate that with failure, or losing a match. Losing this kind of match tells you where you are in your development, and it is a signal to work on something.
Thus, I don’t have specific recommendations other than to lock your door, set appropriate boundaries, and be as polite as you can be.
Good luck.