D.C. Code § 42-3204

A tenancy by sufferance may be terminated at any time by a notice in writing from the landlord to the tenant to quit the premises leased, or by such notice from the tenant to the landlord of his intention to quit on the 30th day after the day of the service of the notice. If such notice expires before any periodic instalment of rent falls due, according to the terms of the tenancy, the landlord shall be entitled to a proportionate part of such instalment to the date fixed for quitting the premises.