In the darkest days of the cold war, the military lied to the American public about the true nature of many unidentified flying objects in an effort to hide its growing fleets of spy planes, a Central Intelligence Agency study says. The deceptions were made in the 1950's and 1960's amid a wave of U.F.O. sightings that alarmed the public and parts of official Washington. The C.I.A. study says the Air Force knew that most reports by citizens and aviation experts were based on fleeting glimpses of U-2 and SR-71 spy planes, which fly extremely high. Rather than acknowledging the existence of the top-secret flights or saying nothing about them publicly, the Air Force decided to put out false cover stories, the C.I.A. study says. For instance, unusual observations that were actually spy flights were attributed to atmospheric phenomena like ice crystals and temperature inversions. ''Over half of all U.F.O. reports from the late 1950's through the 1960's were accounted for by manned reconnaissance flights'' over the United States, the C.I.A. study says. ''This led the Air Force to make misleading and deceptive statements to the public in order to allay public fears and to protect an extraordinarily sensitive national security project.'' The admission of Federal deception on the issue appears to be a first, experts said in interviews. ''It's very significant,'' said Richard Hall, chairman of the Fund for U.F.O. Research, a group in Washington.