McLEAN, Va. — SpaceX CEO Elon Musk and a watchdog group are questioning whether a former senior Air Force contracting official acted inappropriately by taking an executive position with a private contractor just months after awarding a multibillion-dollar rocket-launch contract that greatly benefits his new employer.

Musk, citing an article by the Washington, D.C.-based National Legal and Policy Center, suggested Thursday night on Twitter that the Pentagon inspector general should investigate the actions of former Air Force civilian Roger “Scott” Correll.

Earlier this year, Correll retired from his post as the Air Force’s program executive officer for space launch, where he wielded enormous influence in awarding a multibillion-dollar contract for 36 rocket launches over the next several years, shooting sensitive national-security equipment into space.

The contract went to a company called United Launch Alliance (ULA), a joint venture of the nation’s two biggest weapons contractors — Boeing and Lockheed Martin. Earlier this month, Correll took a job as vice president of government acquisition and policy with Aerojet Rocketdyne, the company that supplies the rocket engines used by ULA.

“Something here smells,” said Peter Flaherty, president of the National Legal and Policy Center. “There are a lot of unanswered questions, and the sums of money involved are so enormous that taxpayers are entitled to some answers.”

Glenn Mahone, a spokesman for Aerojet Rocketdyne, said the allegations surrounding Correll’s hiring are “completely without merit.” He said Correll began working at Aerojet only a week or two ago — well after the contract had been awarded — and that his hiring was vetted and cleared by the Air Force.

Correll did not return phone and email messages seeking comment.

An Air Force spokesman declined to comment Friday, citing ongoing litigation over the contract.

SpaceX, which has been pursuing Air Force certification to compete on rocket-launch contracts, filed a court challenge last month seeking to nullify the contract. Earlier this week, SpaceX amended its complaint to include the allegations surrounding Correll’s involvement.

In a series of tweets Thursday night, Musk said the case “certainly deserves close examination by the (Department of Defense) Inspector General,” which conducts internal investigations.

Musk, a billionaire who founded the PayPal mobile-payment service and is also CEO of electric carmaker Tesla Motors, said via Twitter that Correll “first tried to work at SpaceX, but we turned him down. Our competitor, it seems, did not.”