Persistent Potential Tenant

A few months ago, I had a vacancy and posted the apartment on Zillow. Many people applied, and I offered it to a woman that just met the minimum requirements. A week before move in, she texted me saying that she changed her mind and would not be taking the apartment. So, I offered it to the next person in line. After the 2nd person accepted, she called me back and changed her mind again and would like to take the apartment. I told her it is too late, someone else took it. Good luck in your search.

Now, I have another apartment that is vacant and posted it on Zillow. This same woman has been emailing, calling, and texting me every day, asking about the apartment. I am hesitant to rent to her as she seems very wishy washy and a high maintenance type of person. How do I handle this situation?