We're a bunch of brokers here. This question is better asked of a Real Estate Attorney. New York State does issue a Tenants Rights booklet and I've gone throught it in relation to this question. While there is a discrimination section, there is no specific mention of citizenship or visa status as being discriminatory or a protected class. In this case it might seem inappropriate but it doesn't seem to be discriminatory and if not discriminatory, documentation could be provided.
Again, I would ask an Attorney. BTW, I've not come upon a lease application asking for this status but things are constantly changing and it wouldn't surprise me.