It was not a simple question for the service.

Greitens, 45, admitted to having an extramarital affair but denied accusations that he coerced the woman involved into a sexual act and threatened to publicize a photo of her partially nude if she ever went public with their relationship.

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The charges were dismissed amid allegations of prosecutorial misconduct, and Greitens had a decorated past that included hunting al-Qaeda in combat, founding the veterans nonprofit the Mission Continues and publishing a best-selling book that discussed his service.

Four months later, the Navy is still weighing what to do with Greitens and how it should handle other cases involving alleged misconduct in the future.

While the door has been opened to Greitens continuing to serve, the Navy has not decided whether it will allow him to take a position outside of his home state that he might desire, three Navy officials said, who like others spoke on the condition of anonymity because of the sensitivity of the situation.

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Greitens’s potential reemergence in the military, first reported by the Kansas City Star, has left the Navy facing questions about its judgment in an era in which sexual assault statistics in the military have drawn outrage.

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But in a move that has not previously been reported, the case also has prompted the chief of naval operations, Adm. John Richardson, to call for a new 30-day review of how the service handles personnel cases involving personal misconduct allegations, including Greitens’s.

Richardson, writing May 26 in an email to other admirals, said the “recent events involving the transition of Mr. Greitens” have “excited a persistent frustration of mine that I want to address more comprehensively.” The Navy’s policies and practices for addressing personal misconduct are “too cumbersome and slow,” creating situations where officials end up retaining people “we’d rather see dismissed from our ranks.”

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Such decisions, Richardson concluded, weaken “the ethical fiber of our Navy” and put the service “in a situation that is hard to explain to ourselves, and even more difficult to explain to the American people.”

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In an interview with The Post, Richardson acknowledged sending the email and said he wants to know whether the Navy needs more agility to handle cases of alleged misconduct that fall short of criminal matters.

“It’s a much more broad thing that I think might have been stimulated by this discussion of the Greitens case, but it’s really been simmering,” said Richardson, who will retire this summer. “We have been poking at this issue at different directions for some time.”

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Richardson, asked about the status of Greitens’s future in the Navy, cited the review. “It will all be a part of this thing,” he said.

The admiral’s comments underscore how sensitive it has become for Greitens to put on a uniform again.

The former governor, once seen as a rising star in the Republican Party and as potential presidential timber, resigned last June after he was charged with two felonies: invasion of privacy and tampering with computers. In addition to the accusation involving the nude photograph, prosecutors said he had illicitly used the donor list of the Mission Continues for political fundraising.

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Both charges were dropped, but Greitens resigned under threat of impeachment after a Missouri state investigative committee found the woman credible, according to a report the panel issued. As he left office, Greitens echoed a refrain of President Trump, who endorsed him in his gubernatorial run, calling the prosecution a “political witch hunt.”

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Greitens, reached by The Post on Thursday, declined to comment.

A former senior defense official acknowledged speaking extensively with Greitens about where he might fit and confirmed making inquiries on Greitens’s behalf about whether there was a home for him on the National Security Council’s staff as a military officer.

Warren Lockette, another former defense official and friend of Greitens, said the former governor has been wrestling with what to do with his life and is still driven to serve others.

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“This feeling of service and what he gets out of it, it doesn’t go away,” said Lockette, who served during the Obama administration. “I’m hoping that wisdom prevails, and the politics step aside, and he is allowed to do what he does so well.”

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In January, Kernan — and days later, Greitens — approached the Navy about the former governor returning to active duty. The Navy’s top admiral overseeing personnel, Vice Adm. Robert Burke, spoke with Greitens, and the possibility of Vice President Pence requesting him by name for a military assignment was raised, military documents said.

An official close to Pence denied that the vice president had any interest in bringing on Greitens.

“He was never under consideration to join our staff for any role, nor do we have any knowledge of any discussion within the administration of him joining in any role,” the official said.

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The former senior defense official assisting Greitens said they never brought up the possibility of serving under Pence, and he said he is not sure how that idea was raised.

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Through a spokesman, Kernan declined to comment on his interest in Greitens’s career.

Emails viewed by The Post outline a case in which some admirals expressed concerns about Greitens. In January, an early assessment of whether the service should bring Greitens back on active duty prompted the senior officer in charge of recruiting, Rear Adm. Brendan McLane, to recommend against it.

“The sexual nature of the charges are not in line with our Navy Core Values, and the campaign finance violations not only do not inspire trust and confidence in his integrity, but also represent a real risk from a security clearance perspective,” McLane wrote.

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Greitens was informed he would not be able to transition to active duty. He shared afterward that the charges had been dropped and asked whether he could actively serve instead as a reserve intelligence officer, documents show.

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At the time, he was a member of the Individual Ready Reserve, a part of the service in which members are not paid or required to train and are often referred to as former service members. Greitens sought a shift to the Selective Reserve, which would allow him to take a new role more quickly and with less screening.

The Navy ultimately allowed Greitens to become a general unrestricted line officer at a support center in St. Louis at his current rank, lieutenant commander. It is not clear what role he would fill with that job.

Documents show that the Navy SEALs, with whom he had served previously, were not interested in bringing him back, citing his age and concerns about his character. But Lockette said Greitens actually was not interested in returning as a SEAL anyway.

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Burke wrote to other admirals that an investigation confirmed that all charges were dropped against Greitens without a plea agreement and noted the ongoing investigation into whether prosecutors acted legally.

Burke defended the manner in which the Greitens case was vetted and handled.

“I write Senators and Congressmen several times a month telling them why we can’t do a favor for this or that constituent — based on our team sticking to the established standards and process,” wrote Burke, who was just confirmed by the Senate as the Navy’s next No. 2 officer. “I recommend against bending the process in the other direction because of some incomplete or inaccurate press reporting.”