NASA does do some classified work however, the vast majority of their work is not classified.

NASA policy on communication:

(a) NASA, a scientific and technical agency, is committed to a culture of openness with the media and public that values the free exchange of ideas, data, and information as part of scientific and technical inquiry. Scientific and technical information from or about Agency programs and projects will be accurate and unfiltered.

(b) Consistent with NASA statutory responsibility, NASA will "provide for the widest practicable and appropriate dissemination of information concerning its activities and the results thereof." Release of public information concerning NASA activities and the results of NASA activities will be made promptly, factually, and completely.

(c) To ensure timely release of information, NASA will endeavor to ensure cooperation and coordination among the Agency's scientific, engineering, and public affairs communities.

(d) In keeping with the desire for a culture of openness, NASA employees may, consistent with this policy, speak to the press and the public about their work.

(e) 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.