Can I refuse to rent to someone with a history of bedbugs?

[Barb Niehaus]

Help! I've been in property management for years but haven't run into this problem until now. I had an applicant whose landlord verification came back showing that she had an infestation of bedbugs and roaches. It was treated a few weeks ago but her current landlord is not renewing her lease due to the pest problem and now the applicant is threatening legal action if we don't rent to her.