When you do a credit search on a perspective tenant, have your Broker run a Landlord Tenant check as well. As long as the landlord has reported the issue to the credit bureaus, and won a judgement, this will show. Additionally, any judgements on the credit report should be scrutinized to see if they have to do with rent issues.
That being said, if everything else is in order and looks great, I would permit the tenant to supply a letter of explanation. There are some really bad landlords out there, and so many people share apartments with roommates in NYC that there could be a plausible explanation that you might feel comfortable with if everything else is stellar.
This is where having a trusted Broker screen your tenants might really come in handy,