Given that NASA works with the Department of Defense, on military projects, it is inevitable that they can classify information for security reasons. Furthermore, NASA's policy on the release of information states that NASA is not required by law to disclose all information.
This policy does not authorize or require disclosure of information that is exempt from disclosure under the Freedom of Information Act (5 U.S.C. § 552) or otherwise restricted by statute, regulation, Executive Order, or other Executive Branch policy or NASA policy (e.g., OMB Circulars, NASA Policy Directives). Examples of information not releasable under this policy include, without limitation, information that is, or is marked as, classified information, procurement sensitive information, information subject to the Privacy Act, other sensitive but unclassified information, and information subject to privilege, such as pre-decisional information or attorney-client communications.
For more information NASA's compliance on classified national security information, you can go here.