Nearly a week after prosecutors filed paperwork accusing Joseph Elledge of murdering his wife, no judge has signed an arrest warrant, a necessary step to formally charging anyone with a felony crime.

And in a move that court observers said is highly unusual, Boone County Prosecuting Attorney Dan Knight's office on Thursday filed a legal brief arguing that it had enough evidence for a first-degree murder charge even though the body of Mengqi Ji has not been found.

Elledge is in the Boone County Jail, held on a $500,000 cash-only bond for child abuse and child endangerment, with one count of endangerment accusing him of separating his child from her mother by killing her.

If he were to find enough money to post that bond, or if the charges were dropped, he could not be held because he is still not formally charged with murder or any other crime.

Prosecutors filed two probable cause affidavits Wednesday when they initially sought the arrest warrant and a bond of $5 million. Boone County prosecutors on Thursday filed another document intended to convince a judge to sign the warrant, titled "Suggestions in Support of Probable Cause."

Written by assistant prosecutor Roger Johnson, the document lays out why prosecutors think Elledge should be charged with murder and legal precedents that they say support that position.

Knight did not return an email or phone message asking why the additional filing was necessary or why the warrant has not been signed.

John O'Connor, who represents Elledge in the child abuse and endangerment case, said he could not comment on the filings in the murder case.

Rusty Antel, a former top assistant in the prosecutor's office and now an attorney handling mainly criminal cases, said the document was unique in his experience.

"I have never seen one of these," Antel said.

Under old common law doctrine, said Ben Trachtenberg of the University of Missouri Law School, a person could not be convicted of a murder without a body. In the past 50 years or so, he said, that has changed.

"In the U.S., there have been cases of murder convictions upheld without bodies," Trachtenberg said.

In the document, Johnson cites cases where murder convictions were obtained even when the manner of death could not be determined due to the decomposition of a body.

"The body not having been found at this time does not undermine a finding of probable cause," Johnson wrote.

Mengqi Ji is a Chinese woman who came to Columbia to study at the University of Missouri. She earned a master’s degree in mechanical and aerospace engineering in December 2014 and married Elledge in 2017.

According to documents filed with the murder complaint and in his pending case, Elledge last saw his wife about 11:30 p.m. Oct. 8. She was missing when he awoke at 5 a.m. on Oct. 9 to feed their 1-year-old daughter and left her car, keys and other personal items behind.

Using statements by Elledge during the early stages of the investigation, combined with records obtained from a search of his phone, investigators have pieced together his movements between the time he said he noticed his wife was missing and when he reported her disappearance to police more than 30 hours later.

The documents show investigators believe Elledge lied to them about his movements. Late in the day on Oct. 9, Columbia Police Department detective Alan Mitchell wrote, Elledge drove to Rocheport. He told investigators he turned around and came home but phone records indicate he drove into Cooper County and stopped for about 45 minutes near the Lamine River.

Investigators spent most of two weeks late in the fall searching the Lamine River near the Highway 41 bridge. While cadaver-detecting dogs indicated human decomposition, no body was found.

In the second probable cause statement written by Mitchell, he states he believes Elledge killed his wife by strangling her. Elledge told investigators he gave his wife a backrub while she was on her stomach and he straddled her.

"Joseph being on Mengqi's back would have put Mengqin in a compromising position that would not have allowed her options for defending herself," Mitchell wrote.

In the document supporting the request for a warrant, Johnson wrote that it should be sufficient to prove that Ji is dead and to show evidence Elledge was criminally responsible.

The statements filed in court state that "police have not been able to locate any signs of life for Mengqi since Oct. 8," including no contact with her child, parents or friends, no online activity and no financial activity.

Elledge's travels on the day after he last saw her were to remote locations where he might find a place to dispose of a body, Mitchell wrote.

In the brief asking that the warrant be signed, Johnson wrote that those facts support the allegation that Elledge was responsible for his wife's death.

"Defendant's effort to conceal the body, his delay in reporting, and his motive provide sufficient proof of murder even without the forensic evidence that would come from a body," Johnson wrote.

The other element of a first-degree murder charge is that the accused deliberated on the act before it was committed. Johnson argued in the brief that the actions of Elledge on Oct. 9 show he was trying to conceal his wife's death.

The act of strangulation, Johnson wrote, takes longer than other methods of killing. The courts have held in other cases that deliberation can be inferred where "a defendant commits a murder which, because of the particular method of attack, required some time to complete."

Elledge's threats to prevent Ji from having custody of their daughter — and potential return home to China with her — and his movements on Oct. 9 when police believe he concealed the body, point to deliberation, Johnson wrote.