Personal Tax Information: 

The District of Columbia requires you to file Form FR-127 (PDF) to obtain a 6 month personal income tax extension, whether or not you filed for a federal extension. Filing for a District of Columbia tax extension will not give you more time to pay any tax balance due. Your balance must be paid by April 15 to avoid possible penalties.

For more information, visit the District of Columbia Office of Tax and Revenue website.
https://www.taxpayerservicecenter.com/individual/Ind_Logon.jsp?type=100

Business Tax Information:

The District of Columbia requires that you file for a business state income tax extension, whether you owe state income taxes or expect a refund. If the form is completed accurately and turned in on time, you'll be granted a six month tax extension.

Filing a District of Columbia tax extension does not grant you extra time to pay any tax balance due. Your balance must be paid by your original tax deadline to avoid possible penalties.

For more information, visit the District of Columbia Office of Tax and Revenue website.
http://otr.cfo.dc.gov/otr/site/default.asp