Connect with Veterans Act of 2014 - Directs the Secretary of Veterans Affairs to: (1) establish a program to facilitate outreach to veterans by the Department of Veterans Affairs (VA), the primary agencies of states for the administration of veterans' benefits and services, political subdivisions of states, and Indian tribes; and (2) publicize such program and the benefits to such entities of participating.

Requires the Secretary, to carry out such program, to: (1) establish a national directory of veterans, and (2) share information in the directory with any such entities from whom a participating individual has expressed interest in receiving information.

Prohibits: (1) the Secretary from selling information collected under this Act, (2) the Secretary or any participating entity from sharing such information with a non-participating entity, or (3) any participating entity from using any such information for any political communication or from requiring any participating individual to purchase any product or service.

Requires the Secretary of Defense (DOD) to: (1) provide to each member of the Armed Forces separating from service a form for the collection of information to be included in the directory, (2) ensure that completion of the form is voluntary, and (3) protect the privacy of individuals who submit information and the security of information.

Directs the Secretaries of Defense and Labor to jointly take appropriate steps to integrate the collection of information under this Act into the Transition Assistance Program.