Deputy Defense Secretary Frank C. Carlucci has voluntarily taken a lie detector test as part of a Pentagon investigation to determine who told The Washington Post about a secret report last week. The report said that, as the Joint Chiefs of Staff have translated the Reagan plan to rearm America, it could cost $750 billion more than now projected.

Henry E. Catto Jr., assistant secretary of defense for public affairs, confirmed to The Post yesterday that Carlucci and several other members of the Defense Resources Board, which includes the top Pentagon civilians, have taken the lie detector test so far in the probe.

The Defense Resources Board met last Thursday to hear a briefing from Pentagon research director Richard D. DeLauer about the mismatch between military strategy and the money earmarked to carry it out.

DeLauer used as one of his yardsticks the Joint Strategic Planning Document in which the Joint Chiefs of Staff give their estimate of the forces needed to carry out the policies of their civilian superiors and prepare for contingencies around the world. DeLauer's report estimated it could take up to $750 billion more in fiscal 1983 dollars than the $1.5 trillion already projected for fiscal 1984 through 1988 to buy all those forces.

The Post reported these figures on Friday after confirming with the Pentagon that the part of the DeLauer report it published was accurate. The Post story also reported that Navy Secretary John F. Lehman Jr. took heated exception during the Defense Resources Board discussion to the assertion that there was not enough money in sight to build the 600-ship Navy that President Reagan has set as a goal.

Defense Secretary Caspar W. Weinberger on the Cable News Network "Newsmaker" program broadcast Saturday said "that story was based on classified information presented to the Defense Review sic Board in closed session," adding that the $750 billion represented "a large number of wants unconstrained by any financial restrictions or restraints of what all of the services combined, consolidated, feel they might want to have if there were no fiscal constraints."

Catto, when asked what was so sensitive from a security standpoint about the behind-closed-doors budget discussion, replied that "what is so upsetting to us" was not security breaches but the fact "someone on the team" would talk about what went on.

Catto said that Weinberger has not taken the lie detector test because he was not at the Thursday meeting chaired by Carlucci. Carlucci, former deputy director of the Central Intelligence Agency, ordered the investigation to try to find how The Post learned about what went on during the closed meeting, Catto said.