Though I'd be surprised if it happens, DC's status as a "state" when it comes to transportation funding might cost it Transportation Alternatives Program (TAP) funds because "According to Interim Guidance issued by FHWA on October 22, 2012, state DOTs are not eligible to apply for TAP funds, although local governments, including local DOTs, are eligible." So because DDOT is normally considered the state DOT, they would be ineligible for funding and there is no "local" DOT to ask for it.
The Transportation Planning Board is not, however, treating it that way.
The TPB currently plans to issue a solicitation for projects in D.C. at the same time that the solicitation is released for Maryland and Virginia projects, with the assumption that the District of Columbia, including DDOT, should be considered a local government and thus, District agencies are eligible to apply for TAP funds. DDOT and TPB staff have contacted FHWA to seek guidance regarding this matter.
TAP is the program that funds Safe Routes to Schools, Recreational Trails and Transportation Enhancements. There may be other ways around this since:
Eligible recipients include local governments, regional transportation authorities, transit agencies, natural resource or public land agencies, school districts and agencies, and other appropriate local or regional governmental entities.
Which may mean that money can go through the schools or WMATA or something, but let's hope it doesn't come to that.
The same document, produced by the National Capital Region TPB, spells out a proposal for how projects will solicit money and money will be awarded. It also includes how the various states plan to spend their money in the near future. For example, in Virginia
For FY2013, VDOT has announced that the state’s entire TAP allocation (including suballocations to large urbanized areas) will be used for Transportation Enhancements projects that were selected by Commonwealth Transportation Board (CTB) before MAP-21 was signed. FHWA has indicated to VDOT that this approach is acceptable as long as the MPOs in Transportation Management Areas (including the TPB) concur. TPB staff is proposing that the TPB concur with VDOT’s approach regarding the FY2013 funds