If this is for a rental then each of the landlords / apartment complexes have their own rules. And each look at different aspects of the "borderline" i.e. how did it become borderline? illness, layoff, relationship issues or silly spending. :):)
If this is for purchase, then contact me, i work with some amazing mortgage brokers that know all the New Hampshire programs to get people into home ownership. They can also advise some things you may wish to look at to "clean up" credits issues and equally important some things not to do.
Let me know how I may help you - you are the customer.
Tim Dolan 603-320-6495