In the absence of a written lease, your roommate is considered to have a tenancy at will or (if he is paying rent on a monthly basis), a month to month lease (or a week to week lease if he is paying on a weekly basis).
Attached are the requirements you need to provide him regarding terminating this lease in your state. His rights are that he requires adequate WRITTEN notice regarding your desire to terminate this type of lease. You do not have to give him a reason for doing so:
§ 55-248.37. Periodic tenancy; holdover remedies.
A. The landlord or the tenant may terminate a week-to-week tenancy by serving a written notice on the other at least seven days prior to the next rent due date. The landlord or the tenant may terminate a month-to-month tenancy by serving a written notice on the other at least 30 days prior to the next rent due date, unless the rental agreement provides for a different notice period. The landlord and the tenant may agree in writing to an early termination of a rental agreement. In the event that no such agreement is reached, the provisions of § 55-248.35 shall control.
(1974, c. 680; 1977, c. 427; 1982, c. 260; 2004, c. 123; 2005, c. 805; 2009, c. 663; 2013, c. 563
Gail

