The District of Columbia Code Title 42 Chapter 32 Section 7 allows landlords to enforce the following penalty should a tenant refuse to leave the premises after being properly served:
Refusal to Surrender Possession
If the tenant, after having given notice of his intention to quit as aforesaid, shall refuse, without reasonable excuse, to surrender possession according to such notice, he shall be liable to the landlord for rent at double the rate of rent payable according to the terms of tenancy for all the time that the tenant shall so wrongfully hold over, to be recovered in the same way as the rent accruing before the termination of the tenancy.
DC Code § 42–3207.
See also DC How to Serve a Notice to Quit.