For that matter, there is no application to HUD (the Department of Housing and Urban Development) to become a CDC either.
Corporations providing many different types of programming call themselves CDCs, and many corporations that observers would call community development corporations identify more as something else, such as neighborhood housing corporations, membership-based neighborhood associations that happen to be corporations, nonprofit housing developers, or another title.
You should be aware of a couple of definitional issues though. Many community development corporations want to become CHDOs, or community housing development organizations. A CHDO is interested in providing housing for low- to moderate-income individuals and households.
After being certified, the CHDO is eligible to compete for a pot of money available only to CHDOs through HUD. Specifically the grant money for housing projects, which may be either rehab or new construction, is part of the HOME program.