I live in a rented house in NJ where me and a roommate share the rent for the place. The place goes on a month to month basis and I do have a contract on this place. The house does have its own Kitchen and Bathroom. I would like to know if I could get a tax credit for the rent I am paying while filing for NJ state taxes?

Yes, but you must report your pro-rated share of the rent AND identify your roommate on the NJ state tax return.