Civilian Service Recognition Act of 2011 - Requires the head of an executive agency to: (1) pay the cost of presenting a U.S. flag for an individual who was an agency employee and died of injuries incurred while serving as a federal employee, (2) furnish such flag upon the request of the employee's next of kin or any other individual as determined by the Director of the Office of Personnel Management (OPM), and (3) provide notice to agency employees of the flag benefit provided by this Act. Allows an exemption from the requirements of this Act if an agency head determines that fulfilling such requirements would endanger U.S. national security or require the disclosure of classified information, or that the employee is not entitled to death benefits due to willful misconduct.